Stabilizing controller and observer synthesis for uncertain strongly coupled composite systems

In this paper, a synthesis procedure for designing a full state observer and feedback control law which stabilizes a given uncertain symmetric composite system with strong interconnections is presented by using the Riccati equation approach of Petersen (1985). In the design procedure, the state feedback gain matrices and the observer gain matrices which stabilize the class of systems can be conducted by the solutions of lower-order algebraic Riccati equations. The uncertainties considered in the systems may be time-varying. However the values of the uncertainties are constrained to lie within some known admissible bounds. A feature of the design procedure presented is the fact that it reduces to the standard LQG design procedure for two modified sub-systems of the symmetric composite system under consideration if the system contains no uncertain parameters.