Analysis of Discrete-Time Switched Linear Systems Under Logical Dynamic Switching

The control properties of discrete-time switched linear systems (SLSs) with switching signals generated by logical dynamical systems are studied using the semitensor product (STP) approach. With the algebraic state-space representation (ASSR), the linear modes and the logical generators are aggregated as a system with hybrid states, 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 dynamical systems can generate the desired switching signals are investigated, and necessary and sufficient conditions for the realizability of the desired switching signals are given with respect to the cases of fixed operating time (FOT) switching and finite reference signal switching.