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.     

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.     

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.     

Observer‐Based H∞ Control for Continuous‐Time Networked Control Systems

This paper is concerned with the observer‐based H_∞ control for continuous‐time networked control systems (NCSs) considering packet dropouts and network‐induced delays. The packet dropouts and network‐induced delays in the sensor‐to‐controller (S‐C) channel and network‐induced delays in the controller‐to‐actuator (C‐A) channel are taken into full consideration. By taking the non‐uniform distribution characteristic of the arrival instants of actually adopted controller inputs into account, a new model for continuous‐time NCSs is established. To reduce the conservatism of modelling, a linear estimation‐based measurement output estimation method is introduced. Based on the newly established model and a Lyapunov functional, new controller design methods are proposed. A numerical example is given to illustrate the effectiveness and merits of the derived results.     

Network‐based H∞ control for stochastic systems

This paper investigates the problem of network‐based control for stochastic plants. A new model of stochastic time‐delay systems is presented where both network‐induced delays and packet dropouts are taken into consideration for a sampled‐data network‐based control system. This model consists of two successive delay components in the state, and we solve the network‐based H_∞ control problem based on this model by a new stochastic delay system approach. The controller design for the sampled‐data systems is carried out in terms of linear matrix inequalities. Finally, we illustrate the methodology by applying these results to an air vehicle control problem. Copyright © 2008 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.     

H ∞ preview tracking control of retarded state‐multiplicative stochastic systems

The problem of infinite‐horizon H _∞ state‐feedback tracking control for linear continuous time‐invariant retarded systems with stochastic parameter uncertainties is investigated. Two tracking patterns are considered depending on the nature of the reference signal; that is, whether it is measured online or previewed in a fixed time‐interval ahead. The stochastic uncertainties appear in the dynamics matrices for both the retarded and the non‐retarded states of the system. The delayed system is transformed via the input–output approach, to an uncertain norm‐bounded system. A new method that efficiently yields a min–max strategy to the solution of each of the aforementioned two cases is suggested where, given a specific reference signal, the controller plays against nature, which chooses the maximizing energy‐bounded disturbance. The theoretical results are demonstrated by two examples that show the impact of the delay length and the preview length on the system performance. Copyright © 2013 John Wiley & Sons, Ltd.     

H ∞ filtering for impulsive networked control systems with random packet dropouts and randomly occurring nonlinearities

In this paper, the problem of H _∞ filtering for impulsive networked control systems with random packet dropouts and randomly occurring nonlinearities is investigated. By utilizing an impulsive model, the network‐induced imperfections including packet dropout and delay are described by the Bernoulli distributed sequence. The delay in the model is assumed to be time varying. Moreover, nonlinearity in the model is assumed to satisfy sector‐like nonlinearities. The H _∞ filter is designed by using the linear matrix inequality (LMI) approach and convex optimization technique. The filter gain matrices for the nonlinear networked control systems can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

A new approach to network‐based H∞ control for stochastic systems

This paper deals with the problem of network‐based H_∞ control for a class of uncertain stochastic systems with both network‐induced delays and packet dropouts. The networked control system under consideration is represented by a stochastic model, which consists of two successive delay components in the state. The uncertainties are assumed to be time varying and norm bounded. Sufficient conditions for the existence of H_∞ controller are proposed to ensure exponentially stable in mean square of the closed‐loop system that also satisfies a prescribed performance. The conditions are expressed in the frame of linear matrix inequalities (LMIs), which can be verified easily by means of standard software. Two practical examples are provided to show the effectiveness of the proposed techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer‐based H ∞ control on nonhomogeneous Markov jump systems with nonlinear input

This paper considers the problem of observer‐based H _∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H _∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear H ∞ output feedback control with integrator for polynomial discrete‐time systems

This paper investigates the problem of designing a nonlinear H _∞ output feedback controller for a class of polynomial discrete‐time systems. In general, this problem is hard to be formulated in a convex form because the relation between the control input and the Lyapunov function is always not jointly convex. Therefore, the problem cannot be solved via semidefinite programming (SDP). On the basis of the sum of squares (SOS) approach and incorporation of an integrator into the controller, sufficient conditions for the existence of a nonlinear H _∞ output feedback controller are given in terms of SOS conditions, which can be solved by an SDP solver. In contrast to the existing methods, a less conservative result is obtained. Finally, numerical examples are used to demonstrate the validity of this integrator approach. Copyright © 2013 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.     

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.     

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.