\(H_\infty\) and robust control of interconnected systems with Markovian jump parameters (Q558601)

The authors discuss problems of stochastic stability and stochastic feedback stabilization for decentralized linear interconnected continuous-time systems with jumping parameters described by a discrete-state Markov process. The notion of stochastic decentralized stability is defined and used to design a decentralized state feedback controller guaranting stochastic stability of the overall system. Moreover the authors formulate a problem of robust \(H_\infty\) control for linear interconnected systems with jumping parameters and parametric norm-bounded uncertainties. Both finite and infinite time control horizons are considered and the line of reasoning is based on Lyapunov-type arguments in the stochastic formulation. The synthesis problem is solved in terms of solutions for a set of coupled differential or algebraic Riccati equations. The authors allow also for uncertainties in intensities of parameter jumps.