Robust stabilization and disturbance attenuation: high gain controllers

This paper examines the design of robust observer based controllers with desirable disturbance attenuation properties for uncertain systems with time-varying uncertainty. The problem is separated into the observer design and then the design of a possibly high gain, feedback control law that recovers the desirable properties of the observer. The main emphasis is placed on identifying structural properties of the nominal system or the uncertainty, that guarantee full recovery. All results have elementary proofs, based on the bounded real lemma and its standard extensions and standard Lyapunov stability theory. Depending on the number of sensors and actuators (and the noise levels in the sensors), such high gain observers may not be desirable. They are reminiscent of the breaking the loop at the input or output techniques, found in the LTR literature. In particular, the results here extend the results of the authors (1992) where the uncertainty is assumed to satisfy some form of matching conditions.