Robust state-feedback control for discrete-time descriptor systems with norm-bounded parametric uncertainties

ABSTRACT

This paper deals with a state feedback ${\mathcal{H}}_{\mathrm{\infty }}$ control problem for linear time-invariant discrete-time descriptor systems with norm-bounded parametric uncertainties. To this end, bounded real lemma (BRL) is extended on the class of uncertain descriptor systems. The control design procedure based on the conditions of BRL for uncertain descriptor systems is proposed. Numerical examples are included to illustrate the effectiveness of the present result.

Keywords:

• Descriptor systems
• suboptimal control
• uncertain linear systems
• ${\mathcal{H}}_{\mathrm{\infty }}$ control
• robust performance
• robust control

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Alexey A. Belov http://orcid.org/0000-0002-3126-0206

Olga G. Andrianova http://orcid.org/0000-0002-8407-1046

Additional information

Funding

This work was partially funded by RFBR according to the research projects 18-38-00076, 17-08-00185, and 19-08-00535.