Optimal Guaranteed Cost Control of Discrete-Time Linear Systems subject to Structured Uncertainties

TL;DR

This paper introduces a convex synthesis method for guaranteed cost control of discrete-time linear systems with structured uncertainties, providing necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback.

Contribution

It develops a generalized guaranteed cost control approach for systems with uncorrelated block diagonal uncertainties, expanding the class of systems that can be effectively controlled.

Findings

Convex synthesis for a broader class of uncertain systems.

Necessary and sufficient conditions for state-feedback control.

Comparison showing advantages over standard LQR and existing GCC methods.

Abstract

In this paper, we propose state- and static output-feedback generalized guaranteed cost control (GCC) approaches for discrete-time linear systems subject to norm-bounded structured parametric uncertainties. This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones. It also provides necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback. We also present a comparative study among the proposed controllers, standard Linear Quadratic Regulator, and Guaranteed Cost Controller found in the literature.