A delay-dependent approach to robust generalized H2 filtering for uncertain continuous-time systems with interval delay

This paper is interested in the problem of robust generalized H"2 (GH"2) filtering for uncertain continuous-time systems with a delay in the state and polytopic uncertainty in system matrices. The delay is assumed to vary in an interval with a nonzero lower bound. Based on a new Lyapunov-Krasovskii functional (LKF), by virtue of free-weighting matrix method and the projection lemma, a new sufficient condition for analyzing the robust GH"2 performance of the filtering error system is first derived, and then by employing a simple linearization procedure, a new design method is proposed in terms of a set of linear matrix inequalities. Since no useful term is neglected in estimating the upper bound of the derivative of the LKF and the lower bound of the delay is included in the obtained conditions, the results in the paper are much less conservative than the open ones, which is finally illustrated by a numerical example.

[1]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[2]  Zhicheng Li,et al.  Further results on H∞ filtering for discrete‐time systems with state delay , 2011 .

[3]  Huijun Gao,et al.  Robust L/sub 2/-L/sub /spl infin// filtering for uncertain systems with multiple time-varying state delays , 2003 .

[4]  Emilia Fridman,et al.  An improved delay-dependent H∞ filtering of linear neutral systems , 2004, IEEE Trans. Signal Process..

[5]  Yuanqing Xia,et al.  Robust generalised H 2 and H ∞ static output feedback control for uncertain discrete-time fuzzy systems , 2009 .

[6]  Keith J. Burnham,et al.  Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation , 2001, IEEE Trans. Signal Process..

[7]  Hamid Reza Karimi,et al.  Observer-Based Mixed H2/H∞ Control Design for Linear Systems with Time-Varying Delays: An LMI Approach , 2008 .

[8]  Jianbin Qiu,et al.  A new design of delay‐dependent robust ℋ︁∞ filtering for continuous‐time polytopic systems with time‐varying delay , 2010, International Journal of Robust and Nonlinear Control.

[9]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[10]  S. Mou,et al.  A New Parameter-Dependent Approach to Robust Energy-to-Peak Filter Design , 2007 .

[11]  Reinaldo M. Palhares,et al.  Robust filtering with guaranteed energy-to-peak performance - an LM1 approach , 2000, Autom..

[12]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[13]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[14]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[15]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[16]  Pedro Luis Dias Peres,et al.  Mixed filtering for uncertain linear systems: A linear matrix inequality approach , 2000, Int. J. Syst. Sci..

[17]  Hamid Reza Karimi,et al.  Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties , 2009 .

[18]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[19]  Yuanqing Xia,et al.  Robust filter design for piecewise discrete‐time systems with time‐varying delays , 2009 .

[20]  Edoardo Mosca,et al.  Robust H2 and Hinfinity filtering for uncertain linear systems , 2006, Autom..

[21]  Yang Shi,et al.  Improved robust energy-to-peak filtering for uncertain linear systems , 2010, Signal Process..

[22]  Magdi S. Mahmoud,et al.  Delay-dependent Hinfinity filtering of a class of switched discrete-time state delay systems , 2008, Signal Process..

[23]  P. Peres,et al.  Robust ℋ∞-Filtering Design with Pole Placement Constraint via Linear Matrix Inequalities , 1999 .

[24]  Jie Yang,et al.  New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay , 2008 .

[25]  Carlos E. de Souza,et al.  Robust /spl Hscr//sub /spl infin// filtering for discrete-time linear systems with uncertain time-varying parameters , 2006, IEEE Transactions on Signal Processing.

[26]  Mario A. Rotea,et al.  The generalized H2 control problem , 1993, Autom..

[27]  Biao Huang,et al.  Robust H2/H∞ filtering for linear systems with error variance constraints , 2000, IEEE Trans. Signal Process..

[28]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[29]  Xinghuo Yu,et al.  A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  Guo-Ping Liu,et al.  Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay , 2008, IEEE Transactions on Automatic Control.

[31]  Maurício C. de Oliveira,et al.  H2 and H∞ robust filtering for convex bounded uncertain systems , 2001, IEEE Trans. Autom. Control..

[32]  P. Shi.  Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

[33]  Wen-an Zhang,et al.  Delay-dependent generalized H2 filtering for uncertain systems with multiple time-varying state delays , 2007, Signal Process..

[34]  Pedro Luis Dias Peres,et al.  Robust 𝒽∞ filtering for uncertain discrete-time state-delayed systems , 2001, IEEE Trans. Signal Process..

[35]  Tong Heng Lee,et al.  Observer-based Hinfinity fuzzy control design for T-S fuzzy systems with state delays , 2008, at - Automatisierungstechnik.

[36]  J.C. Geromel,et al.  H/sub 2/ and H/sub /spl infin// robust filtering for convex bounded uncertain systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[37]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[38]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[39]  M. S. Mahmoud,et al.  Robust /spl Hscr//sub /spl infin// filtering for a class of linear parameter-varying systems , 2001 .

[40]  Peng Shi,et al.  Robust filtering for uncertain delay systems under sampled measurements , 1996, Signal Process..

[41]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[42]  Hamid Reza Karimi,et al.  Observer-Based Mixed H₂/H ∞ Control Design for Linear Systems with Time-Varying Delays , 2008 .

[43]  D. Wilson.  Convolution and Hankel operator norms for linear systems , 1989 .

[44]  M. Mahmoud.  Resilient L/sub 2/-L∞ filtering of polytopic systems with state delays , 2007 .

[45]  B. Lohmann,et al.  H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions , 2005 .

[46]  Peng Shi,et al.  Robust filter design for sampled-data systems with interconnections , 1996, Proceedings of Digital Processing Applications (TENCON '96).

[47]  Huijun Gao,et al.  Stability analysis for continuous systems with two additive time-varying delay components , 2007, Syst. Control. Lett..

[48]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[49]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..