Design of Robust Estimated State Feedback Controllers for Time-Varying Uncertain Systems

A computer-aided method for the design of linear robust controller is studied. The control guarantees asymptotic stability of linear uncertain systems with time-varying uncertainties. The control is designed based on the possible bound of the uncertainty. Necessary and sufficient conditions for quadratic stabilisability are formulated. The controller is first designed by a two level optimisation process under the assumption that all states are available. An observer is then added to estimate unknown states. The allowable bound for combined controller-observer system is sought again by another two level optimisation process. Relevant references and proofs can be found in Chen and Chen (1990).