Robust stability and stabilization of uncertain discrete singular time-delay systems based on PNP Lyapunov functional

摘要

The problems of delay-dependent robust stability and stabilization for discrete singular time-delay systems with norm-bounded uncertainties are investigated in this paper. By introducing some non-positive items to compensate the redundant energy caused by the positive items, an improved Lyapunov functional, namely partial non-positive (PNP) Lyapunov functional, is presented for achieving less conservative results. On the basis of the forward difference of this PNP Lyapunov functional, modified strict linear matrix inequality (LMI)-based delay-dependent conditions are established for the singular time-delay system to be regular, causal and stable. By solving these LMIs, an explicit expression for the desired state-feedback control law is obtained. Finally, numerical examples are given to illustrate that the proposed results are effective and less conservative than the existing ones.