LANGUAGE STABILITY AND STABILIZABILITY OF DISCRETE-EVENT DYNAMICAL-SYSTEMS

This paper studies the stability and stabilizability of discrete event dynamical systems (DEDSs) modeled by state machines. Stability and st abilizability are defined in terms of the behavior of the DEDSs, i.e. the language generated by the state machines (SMs). This generalizes e arlier work where they were defined in terms of legal and illegal stat es rather than strings. The notion of reversal of languages is used to obtain algorithms for determining the stability and stabilizability o f a given system. The notion of stability is then generalized to defin e the stability of infinite or sequential behavior of a DEDS modeled b y a Buchi automaton. The relationship between the stability of finite and stability of infinite behavior is obtained and a test for stabilit y of infinite behavior is obtained in terms of the test for stability of finite behavior. An algorithm of linear complexity for computing th e regions of attraction is presented, which is used for determining th e stability and stabilizability of a given system defined in terms of legal states. This algorithm is then used to obtain efficient tests fo r checking sufficient conditions for language stability and stabilizab ility.