Parameterization of all stable controllers stabilizing full state information systems and mixed sensitivity

Abstract

Analytical expressions for the parameterization of all one- and two-degrees-of-freedom stable controllers stabilizing full state information systems are presented. It is assumed that the strictly proper, lumped, and linear time-invariant nominal plant has a stabilizable realization and is strongly stabilizable, and that the number of entries of the plant state is even and is double the number of entries of the plant input. Right and left coprime factorizations of the transfer function of the plant in terms of the matrices of the plant realization are proposed, the Diophantine equation is solved, and stabilizing controllers are obtained using Youla parameterization. Conditions for strong stability are given, and the free parameters of the stabilizing controllers solving the mixed sensitivity problem are established. The results are illustrated through simulation examples of a half-car active suspension system and a two-degrees-of-freedom planar rotational robot.