Delay-Independent Stabilization of Linear Discrete-Time Systems with Uncertain Delay

Abstract

We propose two methods for testing the delay-independent stability of discrete-time systems with unknown delay. Both have LMI form. The first method is based on a polynomial Lyapunov equation that is equivalent to the stability of a parametric matrix. The second method tests the strict positivity of a bivariate matrix polynomial. Both methods are shown to give better results than previous methods. Also, we extend the polynomial Lyapunov function approach to finding a delay-independent stabilizing static output feedback, using an iterative algorithm in which each iteration consists of solving LMIs. The behavior of the algorithm is illustrated with extensive results.