The Linear Constrained Regulation Problem for Some Linear Continuous-Time Singular Systems

Abstract

Abstract A major issue in modem control system design is direct integration of technological and security constraints in the control law. In general, the respect of constraints can be obtained by constructing a stabilizing controller which makes positively invariant a domain included in the set defined by the constraints. In most of practical control problems, state and/or input constraints generate convex polyhedra in the state space. This paper establishes some necessary and sufficient algebraic conditions for positive invariance of a convex polyhedra w.r.t linear continuous-time singular systems. These results can be considered as an extension of the positive invariance relations for linear normal systems. These results are then applied to solve certain constrained control problem, when the inputs are constrained to belong to a compact polyhedron. It is shown that for a controllable singular system with a sufficient number of stable finite poles, it is always possible to construct a stabilizing state feedback control, u(t) = Fx(t) , guaranteeing the closed-loop positive invariance of the' polyhedron determined by the feedback matrix F. A numerical example is given.