Groupe d’études et de recherche en analyse des décisions

# Control for Markovian Jumping Linear Systems with Parametric Uncertainty

## Peng Shi et El-Kébir Boukas

This paper studies the problem of control for linear systems with Markovian jumping parameters. The jumping parameters considered here are two separable continuous-time discrete-state Markov process, one appearing in all system matrices, and one appearing in control variable. Our attention is focused on the design of linear state feedback controllers such that both stochastic stability and a prescribed performance are required to be achieved. We also deal with the robust control problem for linear systems with both Markovian jumping parameters and parameter uncertainties. The parameter uncertainties are assumed to be real time-varying norm-bounded, appearing in the state matrix. Both the cases of finite and infinite horizon are analyzed. We show that the problems of control for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled either differential Riccati equations for finite horizon case, or algebraic Riccati equations for infinite horizon case, respectively. Particularly, robust controllers are also designed when jumping rates have parameter uncertainties.

, 29 pages