Output feedback control using state observers of a class of nonlinear nonstandard two-time-scale systems

This paper develops a theory of output feedback control for a class of nonlinear, nonstandard two-time-scale systems using a controller and a state observer with guaranteed closed-loop stability. Using insights from geometric singular perturbation theory, a sequential controller is designed over two time-scales. For different choices of measurements, Lyapunov-based observer designs are investigated. Both the controller and the observer are designed to guarantee Lyapunov stability of the lower-order reduced subsystems. Using an extension of the composite Lyapunov analysis, it is proved that the full-order nonlinear system with the controller and the observer remains globally asymptotically stable up to a bound of the time-scale separation parameter. In addition, the composite Lyapunov analysis yields sufficient conditions as guidelines to select the gains. The approach and analysis are demonstrated on a nonlinear two-time-scale system for which the reduced subsystems are linear, but the composite Lyapunov analysis handles the nonlinearity present in the full-order dynamics.