Regulator Problem for Singular Linear Systems with Constrained Control

This chapter solves the problem of controlling singular continuous-time systems with constraints on the control magnitude and its rate, by using state and derivative feedback (proportional-derivative controllers). Necessary and sufficient conditions for positive invariance are proposed. The synthesis of the controller is presented using two methods: an exact method based on non-symmetric Riccati equations and an approximate method based on the solution of equation \(XA+XBX=HX\). An example illustrates the feasibility of the proposed approach. As a particular case, the extension to non-singular systems is also presented.