Reduction of H∞ state feedback control problems for the MIMO servo systems

We deal with H_∞ state feedback control problem for the multi‐input‐multi‐output (MIMO) servo system and discuss the advantages of the facial reduction (FR) to the resulting linear matrix inequality (LMI) problems. In fact, as far as our usual setting, the dual of the LMI problem is not strictly feasible because the generalized plant has always stable invariant zeros. Thus FR is available to such LMI problems, and we can reduce and simplify the original LMI problem to a smaller‐size LMI problem. As a result, we observe that the numerical performance of the SDP solvers is improved. Also, as a by‐product, we obtain the best performance index of the reduced LMI problem with a closed‐form expression. This helps the H_∞ performance limitation analysis. Another contribution is to reveal that the resulting LMI problem obtained from H_∞ control problem has a finite optimal value, but no optimal solutions under an additional assumption. This is also confirmed in the numerical experiment of this paper. FR also plays an essential role in this analysis.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.     

LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS

In this paper, the robust delay‐dependent H_∞ control for a class of uncertain systems with time‐varying delay is considered. An improved state feedback H_∞ control is proposed to minimize the H_∞‐norm bound via the LMI optimization approach. Based on the proposed result, delay‐dependent criteria are obtained without using the model transformation technique or bounded inequalities on cross product terms. The linear matrix inequality (LMI) optimization approach is used to design the robust H_∞ state feedback control. Some numerical examples are given to illustrate the effectiveness of the approach.     

Robust H∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems

This paper studies the H_∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems. Firstly, by using the linear matrix inequality (LMI) method, a sufficient condition is obtained for the robustly stochastic stability. Secondly, the robust H_∞ state feedback controller is designed, such that the considered system is not only internally stochastically stabilizable but also satisfies the robust H_∞ performance. The desired robust H_∞ controller is obtained via solving some LMIs. Finally, one example is provided to demonstrate the effectiveness of the proposed method.     

State feedback H∞ control for quantized discrete‐time systems

This paper is concerned with the quantized state feedback H_∞ control problem for discrete‐time linear time‐invariant systems. The quantizer considered here is dynamic and composed of an adjustable “zoom” parameter and a static quantizer. Static quantizer ranges are with practical significance and fully considered here. A quantized H_∞ controller design strategy is proposed with taking quantizer errors into account, where an iterative linear matrix inequality (LMI) based optimization algorithm is developed to minimize static quantizer ranges with meeting H_∞ performance requirement for quantized closed‐loop systems. An example is presented to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐dependent adaptive reliable H∞ control of linear time‐varying delay systems

This paper considers the problem of delay‐dependent adaptive reliable H_∞ controller design against actuator faults for linear time‐varying delay systems. Based on the online estimation of eventual faults, the parameters of adaptive reliable H_∞ controller are updating automatically to compensate the fault effects on the system. A new delay‐dependent reliable H_∞ controller is established using a linear matrix inequality technique and an adaptive method, which guarantees the stability and adaptive H_∞ performance of closed‐loop systems in normal and faulty cases. A numerical example and its simulation results illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

H∞ Model Reduction for Positive Fractional Order Systems

This paper focuses on the H_∞ model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced‐order fractional system such that the associated error system is stable with a prescribed H_∞ performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H_∞‐norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced‐order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.     

H∞ output tracking control for uncertain networked control systems via a switched system approach

In this paper, the problem of H_∞ output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output tracking H_∞ performance analysis is presented, and robust switching H_∞ model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Periodically Time‐Varying Memory State‐Feedback for Robust H2 Control of Uncertain Discrete‐Time Linear Systems

This study is concerned with the synthesis of periodically time‐varying memory state‐feedback controllers (PTVMSFCs) for discrete‐time linear systems. In our preceding studies, we have already established a solid theoretical basis for linear matrix inequality (LMI)‐based (robust) H _∞‐PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H ₂ performance criterion. In the H ₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and the inequalities for bounding traces that characterize the H ₂ norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H ₂‐PTVMSFC synthesis. On the basis of this result, we also consider robust H ₂‐PTVMSFC synthesis for LTI systems with parametric uncertainties.     

ROBUST H∞ CONTROL AND QUADRATIC STABILIZATION OF DISCRETE‐TIME SWITCHED SYSTEMS WITH NORM‐BOUNDED TIME‐VARYING UNCERTAINTIES

We focus on robust H_∞ control analysis and synthesis for discretetime switched systems with norm‐bounded time‐varying uncertainties. Sufficient conditions are derived to guarantee quadratic stability along with a prescribed H_∞‐norm bound. Each of them can be dealt with as a linear matrix inequality (LMI) which can be tested with efficient algorithms. All the switching rules are constructively designed, and do not rely on any uncertainties.     

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

The dissipativity of discrete‐time switched memristive neural networks with actuator saturation is considered in this paper. By constructing a quasi‐time‐dependent Lyapunov function, sufficient conditions are obtained to guarantee the exponential stability and exponential dissipativity for the closed‐loop system with mode‐dependent average dwell time switching. Furthermore, the exponential H_∞ performance of discrete‐time switched memristive neural networks is also analyzed, while the quasi‐time‐dependent controller and observer gains of the desired exponential dissipative and H_∞ performance can be calculated from linear matrix inequalities. Finally, the effectiveness of theoretical results is illustrated through the numerical examples.     

Reliable H ∞ Filtering for Mixed Time‐Delay Systems with Stochastic Nonlinearities and Multiplicative Noises

This paper investigates the reliable H_∞ filtering problem for a class of mixed time‐delay systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time‐varying and distributed delays. The stochastic nonlinearities in the form of statistical means cover several well‐studied nonlinear functions. The multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays, stochastic nonlinearities, and multiplicative noises, sufficient conditions for the existence of a reliable H _∞ filter are derived, such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a guaranteed H _∞ performance level. Then, a linear matrix inequality (LMI) approach for designing such a reliable H _∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

Integrated fault estimation and fault‐tolerant control for uncertain Lipschitz nonlinear systems

This paper proposes an integrated fault estimation and fault‐tolerant control (FTC) design for Lipschitz non‐linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non‐linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H_∞ optimization with a single‐step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single‐link manipulator example is given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed consensus observer-based H∞ control for linear systems with sensor and actuator networks

This paper proposed a distributed consensus observer (DCO) based H_∞ control method for a class of linear time-invariant (LTI) continuous systems with a sensor and actuator network (SAN). The communication topology of the SAN under consideration is represented by a directed graph, in which the sensor nodes are not able to acquire all the control inputs applied to the target system from the actuator nodes. To overcome this difficulty, a set of novel DCOs embedded in the sensor nodes and a set of DCO-based controllers embedded in the actuator nodes are initially constructed to estimate and control the state of the target system in a fully distributed way, respectively. The constructed DCOs take full advantage of their consensus property and replace the unavailable control inputs with the approximate ones computed on the basis of the state estimates of the underlying sensor node and its neighboring sensor nodes. Subsequently, a design method of DCO-based H_∞ control is proposed in terms of bilinear matrix inequality (BMI) to ensure that the closed-loop system is exponentially stable while satisfying a prescribed overall H_∞ performance of disturbance attenuation. Moreover, in order to make attenuation level as small as possible, a suboptimal H_∞ control design problem is formulated as a BMI optimization problem, and a modified path-following method is provided for solving this problem by using the existing linear matrix inequality (LMI) optimization techniques. Finally, simulation results demonstrate the effectiveness of the proposed method.     

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.     

H∞ control of memristive neural networks with aperiodic sampling and actuator saturation

The H_∞ control problem for memristive neural networks with aperiodic sampling and actuator saturation is considered in this paper. A novel approach that is combined with the discrete‐time Lyapunov theorem and sampled‐data system is proposed to cope with the aperiodic sampling problem. On the basis of such method and choosing a polyhedral set, sufficient conditions to determine the ellipsoidal region of asymptotic stability and exponential stability for the estimation error system are obtained through a saturating sampled‐data control. Furthermore, H_∞ performance index of memristive neural networks with disturbance is also analyzed, whereas the observer and controller gains are calculated from stability conditions of linear matrix inequalities. Finally, the effectiveness of the theoretical results is illustrated through the numerical examples.     

H∞ Non‐Fragile Synchronous Guaranteed Control of Uncertainty Complex Dynamic Network with Time‐Varying Delay

A kind of H_∞ non‐fragile synchronization guaranteed control method is put forward for a class of uncertain time‐varying delay complex network systems with disturbance input. The network under consideration includes unknown but bounded nonlinear coupling functions f(x) and the coupling term and node system with time‐varying delays. The nonlinear vector function f(x) need not be differentiable but should satisfy the norm bound. A non‐fragile state feedback controller of the gain with sufficiently large regulation margin is designed. It is ensured that the parameters of the controller could still be effective under small perturbation. The sufficient conditions for the existence of H_∞ synchronous non‐fragile guaranteed control of this system have been obtained by constructing a suitable Lyapunov‐Krasovskii functional, adopting matrix analysis, using the theorem of Schur complement and linear matrix inequalities (LMI). These conditions can guarantee robust asymptotic stability for each node of network with disturbance as well as achieve a prescribed robust H_∞ performance level. Finally, the feasibility of the designed method is verified by a numerical example.     

An Improved Anti‐Windup Bumpless Transfer Structures Design for Controllers Switching

In this paper, an anti‐windup bumpless transfer (AWBT) control structure combined with linear interpolation method is proposed for smooth switching control. By choosing an appropriate scheduling signal, different controllers can be switched smoothly under a unified framework. Meanwhile, some robust specifications including H₂/H_∞ performance, pole placement constraint, and passivity of the closed‐loop system can be preserved through controller switching. Furthermore, for the linear system subject to input saturation, the stability and L₂ gain of the closed‐loop system can be guaranteed. Finally, a cart‐spring pendulum system is simulated to demonstrate the effectiveness of the proposed scheme.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.