Optimal guaranteed cost filtering for Markovian jump discrete-time systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

[1]  Dj.B. Petkovski,et al.  Multivariable Control Systems Design: A case Study of Robust Control of Nuclear Power Plants , 1987 .

[2]  Duncan McFarlane,et al.  Robust state estimation for uncertain systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[3]  Pierre Bertrand,et al.  An image-based filter for discrete-time markovian jump linear systems , 1996, Autom..

[4]  K. Loparo,et al.  Stability and control of discrete-time jump linear systems , 1991 .

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

[6]  Michael Athans,et al.  Command and control (C2) theory: A challenge to control science , 1986 .

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

[8]  M. Fragoso,et al.  Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems , 1995, IEEE Trans. Autom. Control..

[9]  R. Rogers,et al.  An LQ-solution to a control problem associated with a solar thermal central receiver , 1983 .

[10]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[11]  Y. Soh,et al.  Robust Kalman filtering for discrete state-delay systems , 2000 .

[12]  Toader Morozan,et al.  Stability and control for linear systems with jump Markov perturbations , 1995 .

[13]  E. Boukas,et al.  H∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty , 1997 .

[14]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

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

[16]  Alan S. Willsky,et al.  A survey of design methods for failure detection in dynamic systems , 1976, Autom..

[17]  François Dufour,et al.  The filtering problem for continuous-time linear systems with Markovian switching coefficients , 1994 .

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

[19]  Marcelo D. Fragoso,et al.  H ∞ filtering for Markovian jump linear systems , 2002, Int. J. Syst. Sci..

[20]  El-Kébir Boukas,et al.  Manufacturing flow control and preventing maintenance: a stochastic control approach , 1988 .

[21]  Lihua Xie,et al.  Robust H/sub /spl infin// filtering for uncertain systems with sampled-data measurements , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[22]  W. Ames.  Mathematics in Science and Engineering , 1999 .

[23]  Magdi S. Mahmoud,et al.  Robust performance results for discrete-time systems , 1998 .

[24]  D. Bernstein,et al.  Steady-state kalman filtering with an H∞ error bound , 1989, 1989 American Control Conference.

[25]  Lihua Xie,et al.  H ∞ filtering for linear periodic systems with parameter uncertainty , 1991 .

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

[27]  John R. Broussard,et al.  Application of precomputed control laws in a reconfigurable aircraft flight control system , 1989 .

[28]  El-Kébir Boukas,et al.  Robust production and maintenance planning in stochastic manufacturing systems , 1995, IEEE Trans. Autom. Control..

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