A Study of Delay-Dependent Stabilization for Discrete-Time Systems with Time Delays

The problem of stabilization of discrete-time delayed systems is investigated in this paper. Based on Lyapunov-Krasovaii functional approach, a delay-dependent stability condition is derived in terms of linear matrix inequalities (LMIs), for the discrete-time delayed systems. In the derivation of the delay-dependent stability result, the model transformation and bounding certain cross terms are avoided. Although the stability condition is given in terms of LMIs, it is found to be not suitable for control design. As a remedy for this, the stability condition is converted to the equivalent linear matrix inequalities with inverse constraints (ICLMIs) which can be employed in designing controllers. Based on the ICLMIs condition, a new delay-dependent stabilization condition for discrete-time delayed systems is given in terms of ICLMIs, which is tractable numerically by the cone complementarity linearization algorithm. Finally, a numerical example and the comparison with an LMI-based result are given to demonstrate the applicability and the less conservativeness of the proposed approach respectively