ℋ− index for discrete-time stochastic systems with Markovian jump and multiplicative noise

Abstract In this paper, we discuss the ℋ − index problem for stochastic linear discrete-time systems subject to Markovian jump and multiplicative noise, for which, a necessary and sufficient condition for an ℋ − index larger than γ > 0 is given in finite time horizon. It is shown that the ℋ − index larger than a given value is equivalent to the solvability of a certain generalized difference Riccati equation (GDRE). What we have obtained generalizes the results of deterministic systems to stochastic models. Moreover, the ℋ − index problem for s q u a r e systems in infinite horizon is also studied. Finally, some examples are presented to illustrate the effectiveness of the proposed theoretical results.