Robust L1/H∞ control of linear Markovian jump systems

In this paper, the problem of robust L₁/H_∞ control for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated using linear matrix inequality (LMI) approach. The uncertainties are assumed to be norm-bounded. The transition of the jumping parameters is governed by a finite-state Markov process. The purpose is to design a linear state feedback controller which guarantees that the closed-loop system is asymptotically stable and has the different performance constraint corresponding to the different output channel. A sufficient condition for the existence of robust L₁/H_∞ controller is given in terms of a group of LMIs. It is showed that this condition is equivalent to the feasible solution problem of LMI. Its solutions provide a parameterized representation of the controller. Furthermore, the controller design problem is converted into a convex optimization problem subject to LMI constraints, which can easily solved by standard numerical software. Finally, a numerical example is given to illustrate the feasibility of the proposed technique.