Robust state-feedback stabilization of jump linear systems

We consider a linear system subject to Markovian jumps, with a time-varying, unknown-but-bounded transition probability matrix. We derive LMI conditions ensuring various second-moment stability properties for the system. The approach is then used to generate mode-dependent state-feedback control laws which stabilize the system in the mean-square sense. When the transition probability matrix is constant and known, our conditions are necessary and sufficient.

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

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

[3]  D. Sworder,et al.  Introduction to stochastic control , 1972 .

[5]  P. Caines,et al.  Optimal adaptive LQG control for systems with finite state process parameters , 1985, The 23rd IEEE Conference on Decision and Control.

[6]  M. Mariton,et al.  Output feedback for a class of linear systems with stochastic jump parameters , 1985 .

[7]  M. Mariton,et al.  A homotopy algorithm for solving coupled riccati equations , 1985 .

[8]  R. Rishel,et al.  An algorithm for a solution of a stochastic adaptive linear quadratic optimal control problem , 1985, 1985 24th IEEE Conference on Decision and Control.

[9]  W. Hopkins,et al.  Optimal control of linear systems with parameter uncertainty , 1986 .

[10]  Jr. William E. Hokins.  Optimal stabilization of families of linear stochastic differntial equations with jump corfficients and multiplicative noise , 1987 .

[11]  H. Chizeck,et al.  Controllability, observability and discrete-time markovian jump linear quadratic control , 1988 .

[12]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[13]  M. Mariton.  Control of nonlinear systems with Markovian parameter changes , 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]  J. P. Chretien,et al.  μ synthesis by D - K iterations with constant scaling , 1993, 1993 American Control Conference.

[17]  A. S. Hodel,et al.  Homotopy methods for the solution of general modified algebraic Riccati equations , 1993 .

[18]  Stephen P. Boyd,et al.  Method of centers for minimizing generalized eigenvalues , 1993, Linear Algebra and its Applications.

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

[20]  H. Abou-Kandil,et al.  Solution and asymptotic behavior of coupled Riccati equations in jump linear systems , 1994, IEEE Trans. Autom. Control..

[21]  L. El Ghaoui,et al.  Solving non-standard Riccati equations using LMI optimization , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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