Analysis of Discrete-Time Switched Linear Systems under Logic Dynamic Switchings

TL;DR

This paper analyzes the control properties of discrete-time switched linear systems with logic-based switching signals using algebraic methods, providing criteria and algorithms for key system properties and realizability conditions.

Contribution

It introduces a hybrid system framework for SLS with logical dynamic switching, deriving new criteria and algorithms for reachability, controllability, observability, and realizability.

Findings

Criteria for reachability, controllability, observability, and reconstructibility of SLS.

Algorithms for verifying system properties.

Necessary and sufficient conditions for generating desired switching signals.

Abstract

The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) approach. With the algebraic state space representation (ASSR), the linear modes and the logical generators are aggregated as a hybrid system, leading to the criteria of reachability, controllability, observability, and reconstructibility of the SLSs. Algorithms for checking these properties are given. Then, two kinds of realization problems concerning whether the logical dynamic systems can generate the desired switching signals are investigated, and necessary and sufficient conditions for the realisability of the required switching signals are given with respect to the cases of fixed operating time switching and finite reference signal switching.