Abstract
A framework is developed for the control design and stability analysis of state-feedback systems made out of automaton–controller pairs, here referred to as automata control systems. A single theorem, based on the Bellman–Ford algorithm, provides the conditions for the design of the controllers that make a given automaton optimal and stable. The automata approximation of continuous state-space models is also developed for the design of state-feedback controllers that can drive continuous plants. The approximation of continuous plants through automata makes the design of state-feedback controllers independent of the state-space description. No distinction is made in the treatment of linear and nonlinear plants. Controller synthesis and specification of the domains of attraction for the resulting plant–controller pair are systematically obtained for continuous time-invariant state-space models. The application of this framework for the stability analysis of the exact model of a digital filter is presented. The automata approximation is applied to design a single controller that stabilises a forced pendulum around two equilibria. The design of switching controllers using automata approximation is also developed and applied to the longitudinal motion control of an aircraft.
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