Invariant Regulators for a Class of Constrained Linear Systems

Abstract

Stable dynamic systems admit positively invariant domains associated to their Lyapunov functions. Conversely, some domains can be made positively invariant for systems with state feedback controllers designed in such a way that some associated definite non-negative functions are bound to decrease. In particular, this approach can be used to establish conditions on the gain matrix for Linear Constrained Regulation Problems (LCRP). We propose a fixed and a variable regulator easy to compute through linear programming, for a class of contrained linear systems