Stability analysis of discrete-time systems with uncertain delays: A quadratic separation approach

This paper addresses the stability of discrete-time systems presenting uncertain delays. Considering appropriate “uncertain” operators, the system is re-written as a feedback interconnection. LMI conditions for the well-posedness and stability of the interconnection are derived from a quadratic separation framework. It is shown that some conditions are equivalent to standard conditions obtained from classical Lyapunov-Krasovskii functionals. On the other hand, by conveniently bounding the uncertain operator and/or considering more complex operators, it is shown that less conservative results can be obtained.