Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Stability and Stabilization of Networked Control Systems Under Limited Communication Capacity and Variable Sampling

This paper investigates the problem of quantized feedback control for networked control systems (NCSs) with time‐varying delays and time‐varying sampling intervals, wherein the physical plant is a continuous‐time, and the control input is a discrete‐time signal. By using an input delay approach and a sector bound method, the network induced delays, the signal quantization and sampling intervals are presented in one framework in the case of the state and the control input by quantization in a logarithmic form. We exploit a novel Lyapunov functional with discontinuity, taking full advantage of the NCS characteristic information including the bounds of delays, the bounds of sampling intervals and quantization parameters. In addition, it has been shown that the Lyapunov functional is decreased at the jump instants. Furthermore, we use the Leibniz‐Newton formula and free‐weighting matrix method to obtain the stability analysis and stabilization conditions which are dependent on the NCS characteristic information. The proposed stability analysis and stabilizing controller design conditions can be presented in term of linear matrix inequalities, which have less conservativeness and less computational complexity. Four examples demonstrate the effectiveness of the proposed methods.     

Passivity‐based asymptotic stabilization for switched nonlinear systems using the sampled integral stabilization technique

The asymptotic stabilization problem is studied for a cascade connection of passive switched nonlinear systems and a passive switched nonlinear system in this paper. When each subsystem is asymptotically zero state detectable and passive on active time intervals, asymptotic stabilization is achieved via co‐design of switching laws and controllers without damping injection. First, an output‐feedback controller is designed to asymptotically stabilize a cascade connection of two passive switched systems if outputs are measurable. Second, when the output of the first switched system is noisy or unmeasurable, a sampled integral stabilization (SIS) technique is employed to investigate asymptotical stabilization of a cascade connection by measuring only the storage function of the second switched system. Finally, as a special case of a cascade connection, the SIS technique is used to stabilize a passive switched system without damping injection. Under this circumstance, the controller is designed by sampling the integral of the passive output. The two‐link robot manipulator is provided to illustrate the effectiveness of the SIS technique.     

Simultaneous deadbeat tracking control of two plants

The simultaneous deadbeat-tracking control of two plants is developed. The twodegree-of-freedom parametrized asymptotical-tracking controller and simultaneous stabilization problem are applied to derive the simultaneous deadbeat-tracking control of two plants. The conditions for existence are given and the systematic design algorithm of the two-degee-of-freedom controller is proposed such that the simultaneous deadbeat-tracking control of two plants is attained.     

Finite‐time posture stabilization of the unicycle mobile robot using only position information: A discrete‐time sliding mode approach

The posture stabilization of a unicycle mobile robot is useful in executing parking and docking maneuvers. It becomes more advantageous to guarantee the posture stabilization in finite time for a battery operated robot, especially in an application involving multiple robots. This paper addresses the posture stabilization of the unicycle mobile robot in finite time, especially when only the position information is available. We adopt the reaching law approach and design a discrete‐time sliding mode (DSM) controller by finitely discretizing the chained form of the unicycle, using the notion of multirate input sampling. Finite‐time stabilization of the equilibria is achieved by using multirate piecewise continuous inputs. Furthermore, the control inputs are realized using multirate output‐feedback (MROF) technique, wherein the states are estimated using the knowledge of the past fast output samples and immediate past control inputs. The proposed MROF‐DSM strategy avoids undesirable chatter in the system response owing to the nonswitching‐type controller and guarantees the stabilization in finite time. Simulations demonstrate the efficacy of the proposed method.     

Self‐triggered state‐feedback control of linear plants under bounded disturbances

This paper addresses the problem of self‐triggered state‐feedback control for linear plants under bounded disturbances. In a self‐triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self‐triggered control available in the literature, we propose a new self‐triggered control strategy that allows for the consideration of model‐based controllers, a class of controllers that includes as a special case static controllers with a zero‐order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed‐loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd.     

A computational method for simultaneous LQ optimal control designvia piecewise constant output feedback

The paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via periodic piecewise constant feedback gain. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes. Explicit formulas for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantitative analysis and synthesis for networked control systems with non‐uniformly distributed packet dropouts and interval time‐varying sampling periods

This paper is concerned with quantitative analysis and synthesis for a networked control system under simultaneous consideration of non‐uniformly distributed packet dropouts, interval time‐varying sampling periods and network‐induced delays. A new packet dropout separation method is proposed to separate packet dropouts from the lump sum of network‐induced delays and packet dropouts. An interval time‐varying sampling period approach, which is more general than a switched sampling period approach, is presented to model the variation of the sampling period. Then a packet dropout decomposition‐based Lyapunov functional is constructed to drive some stability criteria. Based on these stability criteria, a state feedback controller is designed to asymptotically stabilize the networked system in the sense of mean‐square. Numerical examples are given to illustrate the effectiveness of the obtained results. Copyright © 2013 John Wiley & Sons, Ltd.     

Simultaneous stabilization of full state information Linear Time‐Invariant systems

Single necessary and sufficient stability conditions, are presented, for a common Linear Time‐Invariant (LTI) controller that simultaneously stabilizes each of a given family of LTI plants. It is assumed that the strictly proper, lumped and LTI plants have stabilizable realizations and are strongly stabilizable, and that the state‐space dimensions of the plants do not change, are even and are double the input‐space dimensions of the plants. The stabilizing controller is designed for a nominal plant and its free parameter is fixed assuring stability for all the plants, and assuring a stable controller. The stability conditions for simultaneous stabilization are based on the parity interlacing property, on a matrix that must be unimodular and on an analytical expression of the stabilizing controllers. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Finite‐time fault tolerant control for stochastic parameter systems with intermittent fault under stochastic communication protocol

In this article, the finite‐time fault tolerant control problem is investigated for a class of discrete‐time stochastic parameter systems subject to censored measurements. For the sake of relieving the communication burden, a stochastic communication protocol governed by a Markov chain is employed to determine which actuator has the access to the network at each transmission instant. Moreover, an improved performance index dependent on the predetermined censored threshold is constructed to evaluate the disturbance rejection level of the fault tolerant controller in the simultaneous presence of both external disturbances and censoring effects. The main aim of the addressed problem is to design a fault tolerant controller such that the closed‐loop system satisfies both the stochastically finite‐time boundedness and H_∞ performance requirements. In light of the Lyapunov theory combined with matrix inequalities, some sufficient conditions are derived skillfully, and the desired controller gains are calculated by solving a set of linear matrix inequalities. Finally, two simulation examples are utilized to demonstrate the effectiveness of the developed controller design method.     

Stability analysis and design of nonlinear sampled‐data systems under aperiodic samplings

In this paper, the problem of exponential stability analysis and the design of sampled‐data nonlinear systems have been studied using a polytopic linear parameter‐varying approach. By means of modeling a new double‐layer polytopic formulation for nonlinear sampled‐data systems, a modified form of piecewise continuous Lyapunov‐Krasovskii functional is proposed. This approach provides less conservative robust exponential stability conditions by using Wirtinger's inequality in terms of linear matrix inequalities. The distances between the real continuous parameters of the plant and the measured parameters of the controller are modeled by convex sets, and the analysis/design conditions are given at the vertices of some hyper‐rectangles. In order to get tractable linear matrix inequality conditions for the stabilization problem, we performed relaxation by introducing a slack variable matrix. Under the new stability criteria, an approach is introduced to synthesize a sampled‐data polytopic linear parameter‐varying controller considering some constraints on the location of the closed‐loop poles in the presence of uncertainties on the varying parameters. It is shown that the proposed controller guarantees the exponential stability of the closed‐loop system for aperiodic sampling periods smaller than a known value, ie, maximum allowable sampling period. Finally, the effectiveness of the proposed approach is verified and compared with some state‐of‐the‐art existing approaches through numerical simulations.     

Modeling and quadratic stabilization of a class of linear uncertain time‐varying systems

This paper considers the quadratic stabilization of a class of uncertain linear time‐varying (LTV) continuous‐time plants. The state‐space representation of each plant is based on the physically meaningful assumption of a dynamical matrix containing uncertain elements whose time trajectories are sufficiently smooth to be well described by interval polynomial functions with arbitrarily time varying coefficients. At some isolated time instants, the parameters trajectories can exhibit some first‐kind discontinuities due for example to sharply varying operating conditions. Using a parameter independent Lyapunov function, a quadratically stabilizing dynamic output controller is directly obtained by the solution of some LMIs. A salient feature of the paper is that, unlike all the other existing methods, quadratic stabilization can be achieved over possibly arbitrarily large uncertain domains of parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

Topological entropy and data rate for practical stability: a scalar case

A special class of nonlinear systems, i.e. expanding piecewise affine discrete‐time scalar systems with limited data rate, is used to investigate the role of topological entropy and date rate in a practical stability problem. This special class of nonlinear system as an abstract model is an extension of discrete‐time unstable scalar systems, a well‐known model for quantized feedback design. For such systems with finite quantization levels, how to design a quantized feedback controller to achieve practical stability is considered as a boundability problem. Unlike the existing results about topological entropy for nonlinear stabilization and optimal control for linear systems, for the boundability problem under consideration, the feedback topological entropy defined in this paper is not equal to the minimum number of the quantization interval (i.e. the minimal information rate) and only provides a necessary condition for the boundability of our system under some condition. A necessary and sufficient condition for the boundability is also presented in terms of an inequality related to data rate and the minimum number of quantization intervals. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Multirate sampled‐data stabilization for a class of low‐order lower‐triangular nonlinear systems

This paper investigates the problem of sampled‐data controller design for a class of lower‐triangular systems in the p‐normal form (0<p<1). A multirate digital feedback control scheme is proposed to achieve the global strong stabilization of the sampled‐data closed‐loop system under some assumptions. In the design of the controller, the input‐Lyapunov matching strategy and multirate control approach are combined to obtain better stabilizing performance. Unlike the design method based on the approximate discrete‐time model, our controller is obtained from the exact discrete‐time equivalent model, which does not need to be computed completely. The approximate multirate digital controllers are proved to be effective in the practical implementation. It is shown that, compared with the emulated control scheme, our controller may provide faster decrease of Lyapunov function for each subsystem. This will lead to allow large sampling periods. An illustrative example is provided to verify the effectiveness of the proposed control scheme.     

Sampled‐data control of networked nonlinear systems with variable delays and drops

This paper investigates the stabilization problem of the nonlinear networked control systems (NCSs) with drops and variable delays. The NCS is modeled as a sampled‐data system. For such a sampled‐data NCS, the stability properties are studied for delay that can be both shorter and longer than one sampling period, respectively. The exponential stability conditions are derived in terms of the parameters of the plant and time delay. On the other hand, a model‐based control scheme based on an approximate discrete‐time model of the plant is presented to guarantee the stability of the closed‐loop system subject to variable time delays and packet losses. The performance of the proposed control schemes are examined through numerical simulations of an automated rendezvous and docking of spacecraft system. Moreover, the simulations show that by employing the model‐based controller, a higher closed‐loop control performance can be achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

Discrete‐time network‐based control under scheduling and actuator constraints

This paper is concerned with the solution bounds for discrete‐time networked control systems via delay‐dependent Lyapunov–Krasovskii methods. Solution bounds are widely used for systems with input saturation caused by actuator saturation or by the quantizers with saturation. The time‐delay approach has been developed recently for the stabilization of continuous‐time networked control systems under the round‐robin protocol and under a weighted try‐once‐discard protocol, respectively. Actuator saturation has not been taken into account. In the present paper, for the first time, the time‐delay approach is extended to the stability analysis of the discrete‐time networked control systems under both scheduling protocols and actuators saturation. The communication delays are allowed to be larger than the sampling intervals. A novel Lyapunov‐based method is presented for finding the domain of attraction. Polytopic uncertainties in the system model can be easily included in our analysis. The efficiency of the time‐delay approach is illustrated on the example of a cart–pendulum system. Copyright © 2014 John Wiley & Sons, Ltd.     

Sampled‐data output feedback stabilization for a class of switched stochastic nonlinear systems

This paper investigates a global sampled‐data output feedback stabilization problem for a class of switched stochastic nonlinear systems whose output and system mode are available only at the sampling instants. An observer is designed to estimate the unmeasurable state and thus a sampled‐data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the system mode via a sampler. By choosing an appropriate piecewise Lyapunov function, it is proved that the proposed sampled‐data controller with allowable sampling period can stabilize the considered switched stochastic nonlinear systems under an average dwell‐time condition. Finally, two simulation results are presented to illustrate the effectiveness of the proposed method.     

Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties

This paper investigates the problem of robust ??_∞ static output feedback controller design for a class of discrete‐time piecewise‐affine systems with norm‐bounded time‐varying parametric uncertainties. The objective is to design a piecewise‐linear static output feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop system with a prescribed ??_∞ disturbance attenuation level. Based on a piecewise Lyapunov function combined with S‐procedure, Projection lemma, and some matrix inequality convexifying techniques, several novel approaches to the static output feedback controller analysis and synthesis are developed for the underlying piecewise‐affine systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a family of LMIs parameterized by one or two scalar variables, which are numerically efficient with commercially available software. Finally, three simulation examples are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.