Regulation problem for linear discrete-time delay systems with Markovian jumping parameters and symmetrical constraints

In this paper, we investigate the regulation problem for linear discrete-time delay sustems with Markovian jumps and constrained control. The constraints used hete are of symmetrical inequality type. A sufficiemt condition of stochastic stability of closed loop sustem is derived. We use the positive invariance approach of the common set for all the modes to guarntee the admissibility of the control law. In the case of one mode, we obtain the condition of stability for a linear discrete-time delay system as known in the literature. A numerical example is given to ukkustrate the theoretic results.