H∞ controller design for linear systems with time-invariant uncertainties

This paper considers the problem of designing robust H _∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H _∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H _∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for a class of high-speed sampling uncertain systems

The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> static output feedback control of discrete-time switched polytopic linear systems with average dwell-time

This paper investigates the problem of robust exponential H _∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H _∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler’s lemma and Dualization lemma, some novel conditions for exponential H _∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.     

Delay-dependent robust H ∞ control for uncertain fuzzy Markovian jump systems

This paper is concerned with the problem of delay-dependent robust H _∞ control for uncertain fuzzy Markovian jump systems with time delays. The purpose is to design a mode-dependent state-feedback fuzzy controller such that the closed-loop system is robustly stochastically stable and satisfies an H _∞ performance level. By introducing slack matrix variables, a delay-dependent sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequalities. An illustrative example is finally given to show the applicability and effectiveness of the proposed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. This work is supported by the National Science Foundation for Distinguished Young Scholars of P. R. China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047. Yashun Zhang received the B.S. and M.S. degrees in Control Science and Control Engineering from Hefei University of Science and Technology in 2003 and 2006. He is currently a Ph.D. student in Control Science and Control Engineering, Nanjing University of Science and Technology. His research interests include fuzzy control, sliding mode control and nonlinear control. Shengyuan Xu received the Ph.D. degree in Control Science and Control Engineering from Nanjing University of Science and Technology in 1999. His research interests include robust filtering and control, singular systems, time-delay systems and nonlinear systems. Jihui Zhang is a Professor in the School of Automation Engineering of Qingdao University, China. His main areas of interest are discrete event dynamic systems, production planning and control, and operations research.     

Decentralized robust H<Subscript>∞</Subscript> output feedback control for value bounded uncertain large-scale interconnected systems

In this paper, decentralized robust H_∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H_∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H_∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> consensus control of uncertain multi-agent systems with time delays

This paper is devoted to the robust H _∞ consensus control of multi-agent systems with model parameter uncertainties and external disturbances. In particular, switching networks of multiple agents with general linear dynamics are considered, and uncertain communication delays are also taken into account. It shows that a sufficient condition in terms of linear matrix inequalities (LMIs) is derived for the robust consensus performance with a given H _∞ disturbance attenuation level, and meanwhile the unknown feedback matrix of the proposed distributed state feedback protocol is also determined. A numerical example is included to validate the theoretical results.     

Finite-time disturbance attenuation of nonlinear systems

This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems. Based on the finite time Lyapunov stability theory, some finite-time H _∞ performance criterions are derived. Then the state-feedback control law is designed and the structure of such a controller is investigated. Furthermore, it is shown that the H _∞ controller can also make the closed-loop system satisfy finite-time H _∞ performance for nonlinear homogeneous systems. An example is provided to demonstrate the effectiveness of the presented results.     

H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H1 state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

New reduced-order <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filter design method for discrete-time singular systems with lossy measurements by strict LMI approach

In this paper, the new design problems of full and reduced-order H _∞ filters including static filters are investigated for discrete-time singular systems with lossy measurements. The lossy measurement is described by a stochastic variable satisfying Bernoulli random binary distribution to model the measured output. Being different from the previous results, the filter existence condition by a new Lyapunov function for singular systems with lossy measurements is given using a strict linear matrix inequality (LMI) in terms of all variables. The proposed full and reduced-order H _∞ filter guarantees regularity, causality, and mean-square stochastic stability with a H _∞ performance bound of filtering error singular system. Moreover, it is shown that the reduced-order H _∞ filter design method is general for both singular systems and non-singular systems with lossy measurements. Numerical examples are worked out to illustrate the effectiveness and applicability of the proposed method.