Diagonal stability of a class of discrete-time positive switched systems with delay

TL;DR

This paper develops new criteria for ensuring the stability of a specific class of discrete-time positive systems with delays, using diagonal Lyapunov-Krasovskii functionals, applicable to digital filters and neural networks.

Contribution

It introduces novel feasibility conditions for common and switched diagonal Lyapunov-Krasovskii functionals in delayed positive systems, expanding stability analysis tools.

Findings

Derived linear algebraic inequality conditions for stability

Established spectral conditions for common Lyapunov functionals

Validated approaches with a numerical example

Abstract

A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L--K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete-time models of digital filters and neural networks. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.