Reliable H ∞ filter design for T–S fuzzy model‐based networked control systems with random sensor failure

This paper investigates robust and reliable H _∞ filter design for a class of nonlinear networked control systems: (i) a T‐S fuzzy model with its own uncertainties is used to approximate the nonlinear dynamics of the plant, (ii) a new sensor failure model with uncertainties is proposed, and (iii) the signal transfer of the closed‐loop system is under a networked communication scheme and therefore is subject to time delay, packet loss, and/or packet out of order. Four new theorems are proved to cover the conditions for the robust mean square stability of the systems under study in terms of LMIs, and a decoupling method for the filter design is developed. Two examples, one of them is based on a model of an inverted pendulum, are provided to demonstrate the design method. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer‐based H ∞ control for networked systems with bounded random delays and consecutive packet dropouts

This paper is concerned with the H _∞ control problem for a class of systems with bounded random delays and consecutive packet dropouts that exist in both sensor‐to‐controller channel and controller‐to‐actuator channel during data transmission. A new model is developed to describe possible random delays and packet dropouts by two groups of Bernoulli distributed stochastic variables. To avoid the state augmentation, a full‐order observer‐based feedback controller is designed via LMI approach. Based on the Lyapunov theory, a sufficient condition is provided to guarantee the closed‐loop networked system to be asymptotically mean‐square stable and achieve the prescribed H _∞ disturbance‐rejection‐attenuation level. The simulation examples illustrate the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based H ∞ output tracking control for networked control systems

This paper is concerned with observer‐based H _∞ output tracking control for networked control systems. An observer‐based controller is implemented through a communication network to drive the output of a controlled plant to track the output of a reference model. The inputs of the controlled plant and the observer‐based tracking controller are updated in an asynchronous way because of the effects of network‐induced delays and packet dropouts in the controller‐to‐actuator channel. Taking the asynchronous characteristic into consideration, the resulting closed‐loop system is modeled as a system with two interval time‐varying delays. A Lyapunov–Krasovskii functional, which makes use of information about the lower and upper bounds of the interval time‐varying delays, is constructed to derive a delay‐dependent criterion such that the closed‐loop system has a desired H _∞ tracking performance. Notice that a separation principle cannot be used to design an observer gain and a control gain due to the asynchronous inputs of the plant and the controller. Instead, a novel design algorithm is proposed by applying a particle swarm optimization technique with the feasibility of the stability criterion to search for the minimum H _∞ tracking performance and the corresponding gains. The effectiveness of the proposed method is illustrated by an example. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

In this paper, the problem of finite‐time H _∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H _∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H _∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H _∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H _∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

On designing network‐based H ∞ controllers for stochastic systems

This paper is concerned with network‐based H _∞ stabilization for stochastic systems, where network‐induced delays, packet dropouts, and packet disorders are taken into account simultaneously. The packet disorders arising from both the sampler‐to‐controller channel and the controller‐to‐actuator channel are considered by introducing a logic controller and a logic zero‐order hold. The network‐induced delays and packet dropouts are modeled as a constant delay plus a non‐differentiable time‐varying delay in the input. By employing Lyapunov–Krasovskii functional approach, we establish results that parallel well‐known bounded real Lemmas. More specifically, these results provide conditions to bound the H _∞ level of the system, which means the worst case energy of the output of the system when subjected to a unitary norm deterministic disturbance signal. On the basis of these results, suitable network‐based H _∞ controllers are designed by using cone complementary linearization method. An air vehicle system is finally taken as an example to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential H ∞ filtering for stochastic Markovian jump systems with time delays

This paper investigates the problem of exponential H _∞ filtering for stochastic systems with time delays and Markovian jumping parameters. On the basis of Lyapunov–Krasovskii functional theory and generalized Finsler lemma, a delay‐dependent bounded real lemma is established without using any model transformations, bounding techniques for cross terms, or additional free matrix variables. The obtained bounded real lemma guarantees that the filtering error system is both mean‐square exponentially stable and almost surely exponentially stable with a prescribed H _∞ noise attenuation level. Then an exponential H _∞ filter is designed for stochastic retarded Markovian jump systems in terms of a set of LMIs. Meanwhile, the mathematical equivalence of the proposed method to one recent method is presented, but our proposed method is more computationally efficient with fewer matrix variables than that recent method. The validity of the method is verified by a numerical example.Copyright © 2012 John Wiley & Sons, Ltd.     

Non‐fragile H ∞ control for switched stochastic delay systems with application to water quality process

In this paper, the problem of non‐fragile observer‐based H _∞ control for discrete‐time switched delay systems is investigated. Both data missing and time delays are taken into account in the links from sensors to observers and from controllers to actuators. Because data missing satisfies the Bernoulli distribution, such problem is transformed into an H _∞ control problem for stochastic switched delay systems. Average dwell time approach is used to obtain sufficient conditions on the solvability of such problems. A numerical example and a real example for water quality control are provided to illustrate the effectiveness and potential applications of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential H ∞ filtering for singular systems with Markovian jump parameters

This paper is concerned with the H _∞ filter design for continuous‐time singular systems with Markovian jump parameters, whose system mode is transmitted through an unreliable network. In contrast to the traditionally mode‐dependent or mode‐independent filtering method, a new partially mode‐dependent filter is established via using a mode‐dependent Lyapunov function, where the stochastic property of mode available to a filter is considered. Sufficient conditions for the existence of H _∞ filter are obtained as strict linear matrix inequalities. Finally, numerical examples are used to show the effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust H ∞ filtering for singular time‐delayed systems with uncertain Markovian switching probabilities

This paper is concerned with the robust H _∞ filter design for a class of uncertain singular time‐delayed Markovian jump systems, whose transition rate matrix has elementwise bounded uncertainties. By the LMI approach, a novel bounded real lemma is proposed such that the singular Markovian jump system is robustly exponentially mean‐square admissible with a prescribed H _∞ performance index. Based on this, a sufficient condition for the existence of a robust H _∞ filter is developed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust non‐fragile H ∞ ∕ L2 − L ∞ control of uncertain linear system with time‐delay and application to vehicle active suspension

This paper presents an approach to design robust non‐fragile H _∞ ∕ L₂ ? L _∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H _∞ and L₂ ? L _∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H _∞ controller and L₂ ? L _∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

Robust H ∞ control via a stable decentralized nonlinear output feedback controller

This paper presents a new method to construct a decentralized nonlinear robust H ^∞ controller for a class of large‐scale nonlinear uncertain systems. The admissible uncertainties and nonlinearities in the system satisfy integral quadratic constraints and global Lipschitz conditions, respectively. The decentralized controller, which is required to be stable, is capable of exploiting known nonlinearities and interconnections between subsystems without treating them as uncertainties. Instead, additional uncertainties are introduced because of the discrepancies between nondecentralized and decentralized nonlinear output feedback controllers. The H ^∞ control objective is to achieve an absolutely stable closed‐loop system with a specified disturbance attenuation level. A solution to this control problem involves stabilizing solutions to algebraic Riccati equations parametrized by scaling constants corresponding to the uncertainties and nonlinearities. This formulation is nonconvex; hence, an evolutionary optimization method is applied to solve the control problem considered. Copyright © 2012 John Wiley & Sons, Ltd.     

A generalized robust H ∞ filtering for singular Markovian jump systems and its applications

In this paper, a generalized robust H _∞ filtering method is proposed for a class of singular Markovian jump systems, whose generality is mainly embodied that the desired filter could bear perturbances in terms of uncertainties on its parameter matrices. Firstly, an LMI condition of robust mode‐dependent filter is developed. Based on the given result, a new approach to mode‐independent H _∞ filter is presented, which establishes a direct connection between mode‐dependent and mode‐independent filters. Secondly, when the transition rate matrix is with elementwise bounded uncertainties or partially unknown, sufficient conditions of such robust mode‐dependent and mode‐independent filters are all developed within LMI frameworks. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Robust H∞ control for networked systems with transmission delays and successive packet dropouts under stochastic sampling

This paper is concerned with the H_∞ performance analysis for networked control systems with transmission delays and successive packet dropouts under stochastic sampling. The parameter uncertainties are time‐varying norm‐bounded and appear in both the state and input matrices. If packet loss is considered the same as time delay, when models the networked control systems with successive packet dropouts and delays as ordinary linear system with input‐delay approach, due to sampling period is stochastic, then the delay caused by packet losses is a stochastic variable, which leads to difficulties in the stability analysis of the considered system. However, if we can transform the system with stochastic delay into a continuous system with stochastic parameter, we can solve the problem. In this paper, by assuming that the network packet loss rate and employing the information of probabilistic distribution of the time delays, the stochastic sampling system is transformed into a continuous‐time model with stochastic variable, which satisfies a Bernoulli distribution. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean‐square exponential stability of the system with an H_∞ performance. What's more, an H_∞ controller design procedure is then proposed, and a less conservative result is obtained by taking the probability into consideration. Finally, a numerical simulation example is employed to show the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

H ∞ control for discrete‐time nonlinear Markov jump systems with multiplicative noise and sector constraint

This paper addresses the finite horizon H _∞ control problem for a class of discrete‐time nonlinear Markov jump systems with multiplicative noise and nonlinear feedback device. The system nonlinearity occurs in a random way specified by a Bernoulli process, whereas the actuator and sensor nonlinearities are restricted to a sector region. Both the state and the dynamic output feedback H _∞ controllers are devised in terms of difference LMIs. The proposed approach not only allows the resulting system to achieve a prescribed disturbance attenuation level, but also enables the output of actuator/sensor to meet the designated sector condition. Moreover, it is also shown that our approach is well‐adapted for dealing with the discrete‐time Markov jump systems with saturated actuator and sensor. Finally, a backward iterative algorithm is provided to solve the obtained difference LMIs and a numerical example is presented to verify the efficiency of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

New results on static output feedback H ∞ control for fuzzy singularly perturbed systems: a linear matrix inequality approach

This paper presents the novel approaches of designing robust fuzzy static output feedback H _∞ controller for a class of nonlinear singularly perturbed systems. Specifically, the considered system is approximated by a fuzzy singularly perturbed model. With the use of linear matrix inequality (LMI) methods, two methods are provided to design fuzzy static output feedback H _∞ controllers. The resulted controllers can guarantee that the closed‐loop systems are asymptotically stable and satisfy H _∞ performances for sufficiently small ?. In contrast to the existing results, the proposed approaches have two advantages: (i) the gains of controller are solved directly by a set of ?‐independent LMIs, and therefore, the problem of selecting the initial values in iterative LMIs algorithm can be avoided, and (ii) the smaller control input efforts are needed. The given methods are easy to implement and can be applied to both standard and nonstandard nonlinear singularly perturbed systems. Two numerical examples are provided to illustrate the effectiveness of the developed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Delay‐dependent exponential H ∞ filtering for discrete‐time switched delay systems

In this paper, the problem of delay‐dependent exponential H _∞ filtering for discrete‐time switched delay systems is investigated under average dwell time switching signals. Time delay under consideration is interval time‐varying in the states. By introducing a proper factor to construct a novel Lyapunov‐Krasovskii function and using average dwell time approach, sufficient conditions for the solvability of this problem, dependent on the upper and lower bounds of time‐varying delay, are obtained in terms of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results. Copyright © 2011 John Wiley & Sons, Ltd.