Regulation of linear continuous-time singular systems with constrained states and controls

This article considers the constrained regulation problem (CRP) for linear continuous-time singular systems. The study consists in finding for a completely controllable singular system a linear state feedback control law that eliminates the impulsive behavior of a system and transfers asymptotically to the origin all initial states belonging to some polyhedral subset of the state space while respecting the linear constraints on state and control vectors. The proposed method gives a solution to the CRP for a singular system from a transformation that leads to a problem of positive invariance for a reduced order nonsingular one. Conditions guaranteeing the positive invariance for the whole domain of admissible controls are deduced. It is shown that the solution to the CRP is that of a nonlinear algebraic matrix equation.