ℋ− index for continuous-time stochastic systems with Markov jump and multiplicative noise

Abstract This paper investigates the problem of ℋ − index for stochastic linear continuous-time systems involving Markov jump and multiplicative noise. A set of generalized differential Riccati equations (GDREs) are presented and it is shown that the solvability of GDREs is necessary and sufficient for the feasibility of an ℋ − index larger than γ > 0 . Our results extend the corresponding deterministic cases to stochastic systems. Furthermore, the infinite horizon ℋ − index problem for s q u a r e systems is considered. Finally, the effectiveness of the obtained results is tested by two examples.