Finite State Stabilizing Controllers for Systems with Binary Sensors: A Robust Control Approach

This paper develops a constructive approach for designing finite state controllers to stabilize pairs of unstable, homogeneous second order discrete-time systems with binary sensor measurements: The plant is first approximated by a finite state machine and a bound on the quality of approximation is established. A control law is then designed to robustly stabilize the nominal finite state machine model in the presence of admissible approximation uncertainty. The approach can be iterated by refining the finite approximation until an acceptable guaranteed rate of convergence is attained. The resulting controller consists of a finite state observer for the plant and a corresponding full state feedback switching control law. Several simple examples are presented to illustrate this design procedure.