A matrix-based approach to verifying stability and synthesizing optimal stabilizing controllers for finite-state automata

摘要: Abstract In this paper, we develop a matrix-based methodology to investigate the problems of stability and stabilizability for deterministic finite automaton (DFA) in framework semi-tensor product (STP) matrices. First, discuss equilibrium point (resp., set stability) DFA, i.e., verifying whether or not all state trajectories starting from subset states converge specified states). The necessary sufficient conditions both stabilities are given, respectively. Second, stabilizability) DFA is investigated as issue can be globally locally stabilized states) by permissible state-feedback controller. Based on pre-reachability invariant-subset defined criteria derived, Furthermore, each type stabilizability, controllers case minimal length trajectories, called optimal controllers, characterized using proposed polynomial algorithms. Finally, two examples presented illustrate effectiveness theoretical results.