Analysis of Discrete-Time Switched Linear Systems under Logic Dynamic Switchings
Xiao Zhang, Min Meng, Zhengping Ji
TL;DR
This work addresses discrete-time switched linear systems (SLS) whose switching signals are generated by logical dynamic systems. It advances a semi-tensor product (STP)–based merged-algebraic framework (ASSR) to fuse linear modes with logical generators into a linear-like hybrid model, and derives necessary and sufficient criteria and practical algorithms for reachability, controllability, observability, and reconstructibility under logic-driven switching. It further introduces ell-step input-state reachability and develops two realization scenarios—fixed operating times and finite reference-signal tracking—together with an illustrative example validating the approach. The results enable systematic design and verification of controllers where logical networks govern mode switching, with potential impact on cyber-physical systems and complex hierarchical control architectures.
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.