Robust Control Analysis and Design for Discrete-time Singular Systems*t

Abstract—In this paper for the class of continuous time non linear uncertain singular time delay dynamical systems we present robust stability analyze results. Next, we consider a control problem for non linear continuous time uncertain singular time delay dynamical systems involving a notion of optimality with respect to an auxiliary cost which guarantees abound on the worst-case value of an on linear-non quadratic cost criterion over a prescribed uncertainty set. Further we specialize result to affine uncertain systems to obtain controllers predicate do nan inverse optimal control problem. In particular, to avoid the complexity in solving the steady state Hamilton-Jacobi-Bellman equation we parameterize a family of stabilizing controllers that minimize some derived cost functional that provides flexibility in specifying the control law. The performance integrand is shown to explicitly depend on the continuous time non linear singular time delay system dynamics, the Lyapunov function of the closed-loop system, and the stabilizing feed back control law where in the coupling is introduced via the Hamilton-Jacobi-Bellman equation. By varying the parameters in the Lyapunov function and the performance integrand, the proposed framework can be used to characterize a class of globally stabilizing controllers that can meet the closed-loop system response constraints. Obtained results for non linear case are further specialized to continuous time linear singular time delay dynamical systems.