Robust ℋ︁∞ filtering for uncertain Markovian jump linear systems

This paper investigates the problem of ℋ︁∞ filtering for a class of uncertain Markovian jump linear systems. The uncertainty is assumed to be norm‐bounded and appears in all the matrices of the system state‐space model, including the coefficient matrices of the noise signals. It is also assumed that the jumping parameter is available. We develop a methodology for designing a Markovian jump linear filter that ensures a prescribed bound on the ℒ︁2‐induced gain from the noise signals to the estimation error, irrespective of the uncertainty. The proposed design is given in terms of linear matrix inequalities. Copyright © 2002 John Wiley & Sons, Ltd.

[1]  Diffusion Processes and their Sample Paths. , 1968 .

[2]  D. Sworder.  Feedback control of a class of linear systems with jump parameters , 1969 .

[3]  W. Wonham.  Random differential equations in control theory , 1970 .

[4]  Jitendra K. Tugnait,et al.  Detection and estimation for abruptly changing systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[5]  M. Mariton.  Jump Linear Quadratic control with Random state discontinuities , 1987, Autom..

[6]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[7]  M. Fragoso,et al.  On a partially observable LQG problem for systems with Markovian jumping parameters , 1988 .

[8]  D. Bernstein,et al.  Steady-state Kalman filtering with an H ∞ error bound , 1989 .

[9]  U. Shaked,et al.  Game theory approach to optimal linear estimation in the minimum H/sup infinity /-norm sense , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[10]  Uri Shaked,et al.  H/sub infinity /-minimum error state estimation of linear stationary processes , 1990 .

[11]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[12]  J. Speyer,et al.  A Linear-Quadratic Game Approach to Estimation and Smoothing , 1991, 1991 American Control Conference.

[13]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[14]  H. Chizeck,et al.  Jump Linear Quadratic Gaussian Control in Continuous Time , 1991, 1991 American Control Conference.

[15]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[16]  Lihua Xie,et al.  H∞ estimation for uncertain systems , 1992 .

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

[18]  O. Costa.  Linear minimum mean square error estimation for discrete-time Markovian jump linear systems , 1994, IEEE Trans. Autom. Control..

[19]  Lihua Xie,et al.  On robust filtering for linear systems with parameter uncertainty , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[20]  Minyue Fu,et al.  Robust 𝒽∞ filtering for continuous time varying uncertain systems with deterministic input signals , 1995, IEEE Trans. Signal Process..

[21]  計測自動制御学会,et al.  Proceedings of the 35th IEEE Conference on Decision and Control : December 11-13, 1996, Portopia Hotel and International Convention Center, Kobe, Japan , 1996 .

[22]  H. McKean,et al.  Diffusion processes and their sample paths , 1996 .