Optimal guaranteed cost control of discrete-time linear systems subject to structured uncertainties

ABSTRACT

In this paper, we propose state- and static output-feedback generalised 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.

KEYWORDS:

• Robust control
• optimal control
• uncertain systems
• linear systems
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Carlos M. Massera http://orcid.org/0000-0001-6926-511X

Marco H. Terra http://orcid.org/0000-0002-4477-1769

Notes

1. The source code for both numerical examples are available at: https://gitlab.com/cmasseraf/gcc_structured_uncertainty