Robust /spl Hscr//sub /spl infin// filtering for discrete-time linear systems with uncertain time-varying parameters

This paper deals with the problem of robust /spl Hscr//sub /spl infin// filtering for linear discrete-time state-space models with uncertain time-varying parameters. The parameters enter affinely into the state-space model matrices, and their admissible values and variations are assumed to belong to given intervals. A method is derived for designing a linear stationary asymptotically stable filter with a prescribed /spl Hscr//sub /spl infin// performance, in spite of large parameter uncertainty. The proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a Lyapunov function with quadratic dependence on the parameters. The filter design is given in terms of linear matrix inequalities.

[1]  Alexandre Trofino,et al.  Biquadratic stability of uncertain linear systems , 2001, IEEE Trans. Autom. Control..

[2]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .

[3]  U. Shaked,et al.  H/sub infinity /-optimal estimation: a tutorial , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

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

[5]  K. Nishiyama,et al.  Robust estimation of a single complex sinusoid in white noise-H∞ filtering approach , 1999, IEEE Trans. Signal Process..

[6]  Lihua Xie,et al.  H∞ estimation for discrete-time linear uncertain systems , 1991 .

[7]  Georgios B. Giannakis,et al.  Signal processing advances in wireless and mobile communications , 2000, IEEE Signal Process. Mag..

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

[9]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

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

[11]  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.

[12]  U. Shaked,et al.  Game theory approach to state estimation of linear discrete-time processes and its relation to H∞ -optimal estimation , 1992 .

[13]  C.E. de Souza,et al.  Bi-quadratic stability of uncertain linear systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[14]  Alexandre Trofino,et al.  H∞ FILTERING FOR DISCRETE-TIME PIECEWISE LINEAR SYSTEMS , 2004 .

[15]  Lihua Xie,et al.  Robust filtering for a class of discrete-time uncertain nonlinear systems: AnH∞ approach , 1996 .

[16]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

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

[18]  Maurício C. de Oliveira,et al.  H[sub 2] and Hinfinity Robust Filtering for Discrete-Time Linear Systems , 2000, SIAM J. Control. Optim..

[19]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

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

[21]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[22]  Alexandre Trofino,et al.  Robust ℋ℞ filtering for linear discrete-time state-space models with uncertain time-varying parameters , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[23]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..