On output regulation in state-constrained systems: An application to polyhedral case

This paper deals with the problem of output regulation using the state feedback control laws for a class of nonsmooth dynamical systems where the state is constrained to evolve within some convex set. The formalism of differential inclusions (DIs) is used to describe the system dynamics and the derivation of the state feedback law is based on the internal model principle. We study two types of control laws: firstly, a static control is designed assuming that the entire states of the plant and the exosystem are available for feedback; In the second case, only the error to be regulated is available for feedback and a dynamic compensator is designed. The analyses are based on using the properties of the normal cones associated with convex sets to study the well-posedness (existence and uniqueness of solutions) and the stability of the closed-loop system. As an application, we design a discontinuous controller which guarantees the viability of a predefined polyhedral subset of the state space using the formulation of linear complementarity systems.

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