Strong stability for multivariable LTI systems

Abstract

In a proposed Observer-Controller Feedback Configuration (OCFC), a class of proper multivariable causal Linear Time-Invariant (LTI) square systems with a detectable and stabilizable realization, is considered. This configuration is based on pseudo-inverses of the input and output matrices, as well as linear robust pre-compensator $K_{1}(s)$ and dual post-compensator $K_{2}(s)$ stabilizing a full actuation full information plant. $K_{1}(s)$ and $K_{2}(s)$ are low-complexity controllers that belong to the Family of All Stabilizing Controllers (FASC) and their free control parameters are selected to achieve strong stability. The separation principle is fulfilled, and necessary and sufficient stability conditions are provided for the overall system to achieve a stable closed-loop system and stable controller. An algebraic approach is used to find these stability conditions that are useful for the pole placement control problem. A simulation of a mechanical system is used to demonstrate the findings.