Static output-feedback peak-to-peak gain control of discrete-time positive linear systems with diverse interval delays

Abstract

In this article, the problem peak-to-peak gain control (also known as ${\ell }_{\infty }$ -gain control) via static output-feedback scheme is studied for discrete-time positive linear systems with diverse interval delays. By novel comparison techniques involving steady states of upper- and lower-scaled systems with peak values of exogenous disturbances, a characterization for ${\ell }_{\infty }$ -induced norm of the input–output operator is formulated. The obtained characterization is then utilized to derive necessary and sufficient conditions subject to ${\ell }_{\infty }$ -induced performance with prescribed attenuation level. On the basis of the analysis results, and based on a vertex optimization technique, a complete solution to the synthesis problem of a static output-feedback controller that minimizes the worst case amplification from disturbances to regulated outputs subject to peak-to-peak gain is addressed. The derived stabilization conditions are formulated in terms of tractable linear programming conditions, which can be effectively solved by various convex algorithms. Numerical examples and simulations are given to illustrate the effectiveness of the proposed method.