Decentralized weighted control for a class of large‐scale systems with multi‐modes

In this paper, the control synthesis problem for a class of large‐scale systems with multi‐modes that are called large‐scale switched systems is addressed. By introducing the concept of decentralized switching signal and the relevant decentralized average dwell time, the asymptotic stability and weighted ?₂ gain performance are investigated. It should be noted that the decentralized switching covers general switching cases for large‐scale switched systems, namely, it admits both time‐dependent switching signal and arbitrary switching signal blended in the decentralized switching. Then, on the basis of the analysis results, the decentralized weighted control scheme including state feedback controller gains and switching signals is studied. Several design algorithms are proposed to meet different controller design problems. Finally, numerical examples are provided to illustrate theoretical findings within this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis and control of switched linear systems via modified Lyapunov–Metzler inequalities

This paper addresses analysis and switching control problems of continuous/discrete‐time switched linear systems. A particular class of matrix inequalities, the so‐called Lyapunov–Metzler inequalities, will be modified to provide conditions for stability analysis and output feedback control synthesis under a relaxed min‐switching logic. The switching rule combined with switching output feedback controllers will be designed to stabilize the switched system and satisfy a prespecified gain performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in min‐switching based designs. The effectiveness of the proposed approach will be illustrated through numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.     

Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

This paper focuses on the problem of finite‐time $H_{\infty }$ control for one family of discrete‐time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete‐time close‐loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite‐time boundedness and sliding mode $H_{\infty }$ finite‐time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Decentralized filtered feedback linearization for uncertain nonlinear systems

This paper presents decentralized filtered feedback linearization (D‐FFL), which is a decentralized controller for uncertain nonlinear systems with potentially unknown disturbance. Moreover, D‐FFL uses only local‐state feedback (or, in certain cases, local‐output feedback) and local reference‐model‐input feedforward and requires limited model information. For sufficiently small initial conditions and sufficiently large choice of a scalar control parameter, D‐FFL makes the norm of the command‐following error arbitrarily small.     

Robust passivity based resilient control for networked control systems with random gain fluctuations

The problem of resilient controller design for a class of networked control system based on passivity theory is presented. By using the Lyapunov–Krasovskii stability theory and linear matrix inequality approach, a set of sufficient conditions for the existence of state feedback controllers is derived. The networked control system under consideration is modeled by taking the network‐induced imperfections like packet dropouts and transmission delays as a single time‐varying delay. The controller is considered with a stochastic fluctuations in its gain matrix by using the Bernoulli distributed white sequence with time‐varying probability measures. The probability‐dependent sufficient conditions are established to guarantee the resulting closed‐loop system to be stochastically stable with a prescribed mixed and passivity performance criterion. The results are expressed in the form of convex optimization problem subject to the set of LMIs, which can be easily solved by using some standard numerical packages. Finally, a numerical example by using the high‐incidence research model is presented to illustrate the effectiveness and applicability of the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed control of linear time‐varying systems interconnected over arbitrary graphs

In this paper, we focus on designing distributed controllers for interconnected systems in situations where the controller sensing and actuation topology is inherited from that of the plant. The distributed systems considered are composed of discrete‐time linear time‐varying subsystems interconnected over arbitrary graph structures. The main contribution of this paper is to provide results on general graph interconnection structures in which the graphs have potentially an infinite number of vertices. This is accomplished by first extending previous machinery developed for systems with spatial dynamics on the lattice . We derive convex analysis and synthesis conditions for design in this setting. These conditions reduce to finite sequences of LMIs in the case of eventually periodic subsystems interconnected over finite graphs. The paper also provides results on distributed systems with communication latency and gives an illustrative example on the distributed control of hovercrafts along eventually periodic trajectories. The methodology developed here provides a unifying viewpoint for our previous and related work on distributed control. Copyright © 2013 John Wiley & Sons, Ltd.     

Network‐based robust event‐triggered control for continuous‐time uncertain semi‐Markov jump systems

This article investigates the event‐triggered (ET) states feedback robust control problem for a class of continuous‐time networked semi‐Markov jump systems (S‐MJSs). An ET scheme, which depends on semi‐Markov process, is presented to design a suitable controller and save communication resources. To cope with the network transmission delay phenomenon, a time‐delay S‐MJSs model under the ET scheme is introduced to describe this phenomenon. Then, it is assumed that the communication links between event detector and zero‐order holder are imperfect, where the signal quantization and the actuator fault occur simultaneously. The sufficient conditions are derived by means of linear matrix inequalities approach, which guarantees the stochastic stability of the constructed time‐delay S‐MJSs in an optimized performance level. Based on these criteria, the parameters of controller under the ET scheme are readily calculated. Some simulation results with respect to F‐404 aircraft engine system for two kinds of ET parameters are given to validate the proposed method.     

Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete‐time state observations

This study investigates the stabilization issue of stochastic coupled systems with Markovian switching via feedback control. A state feedback controller based on the discrete‐time observations is applied for the stabilization purpose. By making use of the graph theory and the Lyapunov method, we establish both Lyapunov‐ and coefficient‐type sufficient criteria to guarantee the stabilization in the sense of stability, and then, we further develop the mean‐square asymptotical stability. In particular, the upper bound of the duration between 2 consecutive state observations is well formulated. Applications to a concrete stabilization problem of stochastic coupled oscillators with Markovian switching and some numerical analyses are presented to illustrate and to demonstrate the easy verifiability, effectivity, and efficiency of our theoretical findings.     

Adaptive asymptotic stabilization of switched parametric strict‐feedback systems with switched control

This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise virtual control function is given to remove the restriction where some bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach.     

Performance improvement of SISO linear control systems by hybrid state resetting and sector confinement of trajectories

Reset control techniques have been proposed to overcome fundamental limitations of linear controllers by means of their transformation into hybrid models that combine continuous flow and discrete jump dynamics. The hybrid nature in the control loop involves some difficulties when analyzing the performance of the controller and some drawbacks on the controller design related to the stability conditions. The technique that we propose is based on sector confined target dynamics of the continuous flow mode by means of the application of the discrete reset jumps. This behavior, in the error plane , is correlated with certain preferred sectors that lead to fast and over‐damped responses. The paper studies how to design a hybrid resetting version of a linear controller that achieves the required fast and over‐damped responses to arbitrary references. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

This paper addresses the passivity‐based control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Orbital feedback linearization for multi‐input control systems

A nonlinear control system is said to be orbital feedback linearizable if there exist an invertible static feedback and a change of time scale (depending on the state) which transform the system into a linear system. We give geometric necessary and sufficient conditions describing multi‐input control‐affine systems that are orbital feedback linearizable out of equilibria and in the case of equal controllability indices. We also describe a construction of the time rescaling needed to orbitally linearize the system. Moreover, we analyze close relations between orbital feedback linearizable control‐affine systems and control‐linear systems that are feedback equivalent to a multi‐chained form comparing geometric structures corresponding to both problems. We illustrate our results by two examples, one being a rigid bar moving in .Copyright © 2014 John Wiley & Sons, Ltd.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Observer‐based controllers with data dropout rate adaptation

In this work, we address the observer‐based control problem for networked control systems with an unknown time‐varying packet arrival rate (PAR) and under root mean square‐norm bounded disturbances. We assume packetized transmissions of both measurement and control input through a communication network with successful delivery acknowledgement. Using the measurement reception state and the control transmission acknowledgement, we derive a filter to estimate the PAR. We consider that the PAR changes sporadically from a constant value to another one; that is, it has two different behaviours: transient and steady state. While the observer only updates the state estimation using the current received measurements, the controller computes the control action employing the current state estimation and the previous applied control input. We propose to schedule both the observer and controller with rational functions of the PAR estimation. We show that the separation principle applies, and then, seeking higher performance accuracy, we develop an optimization observer and controller design procedure that considers the two possible behaviours of the PAR. This optimization procedure attempts to maximize the estimation and control performances for each of the possible constant values of the PAR while offering robustness against PAR estimation errors and variations of the PAR. By exploiting sum‐of‐squares decomposition techniques, the design procedure involves an optimization problem over polynomials. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Stability and stabilization for stochastic Cohen‐Grossberg neural networks with impulse control and noise‐induced control

By applying the It formula, the Gronwall inequality, and the law of large numbers technique, a new simple sufficient inequality condition is presented for the almost surely exponential stability of the stochastic Cohen‐Grossberg neural networks with impulse control and time‐varying delays. Moreover, a new result is also given for the existence of unique states of the systems. An impulsive controller and a suitable noise controller are also given at the same time. The condition contains and improves some of the previous results in the earlier references.     

New results on stability of singular stochastic Markov jump systems with state‐dependent noise

This paper aims to develop the stability theory for singular stochastic Markov jump systems with state‐dependent noise, including both continuous‐time and discrete‐time cases. The sufficient conditions for the existence and uniqueness of a solution to the system equation are provided. Some new and fundamental concepts such as non‐impulsiveness and mean square admissibility are introduced, which are different from those of other existing works. By making use of the ‐representation technique and the pseudo inverse E⁺ of a singular matrix E, sufficient conditions ensuring the system to be mean square admissible are established in terms of strict linear matrix inequalities, which can be regarded as extensions of the corresponding results of deterministic singular systems and normal stochastic systems. Practical examples are given to demonstrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

A less conservative approach to handle time‐varying parameters in discrete‐time linear parameter‐varying systems with applications in networked control systems

This article proposes a new strategy to deal with linear parameter‐varying discrete‐time systems, whose time‐varying parameters can be written as solutions (such as exponential, trigonometric, or periodic function) of a linear difference equation (DE). The novelty is to explicitly exploit the precise knowledge of the function describing the time‐varying parameter by incorporating the associated DE in the conditions, providing less conservative results when compared with conventional approaches based on bounded or arbitrary rates of variation. The advantage of the method comes from the fact that, differently from the available methods, the pointwise stability for the whole domain of the time‐varying parameters is not a necessary condition to obtain feasible solutions. The applicability and benefits of the proposed technique are investigated in terms of numerical examples concerning robust stability analysis,  filtering, and  state‐feedback control. As a final contribution, the problem of time‐varying sampling periods in the context of networked control systems is investigated using the proposed strategy. A numerical example based on a practical application is presented to illustrate the superiority of the approach when compared to methods from the literature based on matrix exponential computation.