Parameter-dependent robust H∞ filtering for uncertain discrete-time systems

This paper is concerned with the problem of parameter-dependent H"~ filtering for discrete-time systems with polytopic uncertainties. The uncertain parameters are supposed to reside in a polytope. Being different from previous results in the quadratic framework, the parameter-dependent Lyapunov function is used in this paper. Both full- and reduced-order filters are designed, which guarantee the asymptotic stability and a prescribed H"~ performance level. The filter parameters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method.

[1]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

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

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

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

[5]  E. Sánchez,et al.  OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS , 2007 .

[6]  J. Bernussou,et al.  A new robust D-stability condition for real convex polytopic uncertainty , 2000 .

[7]  M. Grimble,et al.  A New Approach to the H ∞ Design of Optimal Digital Linear Filters , 1989 .

[8]  Yuanqing Xia,et al.  Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals , 2003, Syst. Control. Lett..

[9]  Alexandre Trofino,et al.  Robust H2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions , 2005, Syst. Control. Lett..

[10]  Maurício C. de Oliveira,et al.  Robust Filtering of Discrete-Time Linear Systems with Parameter Dependent Lyapunov Functions , 2002, SIAM J. Control. Optim..

[11]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[12]  Alexandre Trofino,et al.  Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems , 2006, IEEE Transactions on Automatic Control.

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

[14]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[15]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[16]  Masayuki Sato.  Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions , 2006, Autom..

[17]  Peng Shi,et al.  Nonlinear H filtering of sampled-data systems , 2000, Autom..

[18]  David Zhang,et al.  Improved robust H2 and Hinfinity filtering for uncertain discrete-time systems , 2004, Autom..

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

[20]  James Lam,et al.  Parameter-dependent filter design with guaranteed H-infinity performance , 2005 .

[21]  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.

[22]  Yuanqing Xia,et al.  Robust stability functionals of state delayed systems with polytopic type uncertainties via parameterdependent Lyapunov functions , 2002 .

[23]  John N. Tsitsiklis,et al.  A survey of computational complexity results in systems and control , 2000, Autom..

[24]  M. Konishi,et al.  Optimal Water Cooling Control for Plate Rolling , 2007, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

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