Analysis of PWA control of discrete-time linear dynamics in the presence of variable time-delay

This paper focuses on the robustness problem for a specific class of dynamical systems, namely the piecewise affine (PWA) systems, defined over a bounded region of the state-space χ. We will be interested in PWA systems emerging from linear dynamical systems controlled via feedback channels in the presence of varying transmission delays by a PWA controller defined over a polyhedral partition of the state-space. We exploit the fact that the variable delays are inducing some particular model uncertainty. Our objective is to characterize the delay invariance margins: the collection of all possible values of the time-varying delays for which the positive invariance of χ is guaranteed with respect to the closed-loop dynamics. These developments can be useful for the analysis of different design methodologies and in particular for predictive control approaches. The proposed delay margins describes the admissible transmission delays for an MPC implementation. From a different perspective, it further provides the fragility margins of an MPC implementation via the on-line optimization and subject to variable computational time.