Observers for stabilization and disturbance attenuation in uncertain systems

Examines the ability to recover the robust disturbance attenuation properties of full state controllers when observers are used to estimate the state. The main emphasis is placed on identifying structural properties of the nominal system or the uncertainty, that guarantee full recovery. Such information can be used for control law design - by separating the controller and observer design - or for improving the system performance by identifying the appropriate number and location of the sensors. The results presented extend the results of (Jabbari and Schmitendorf, 1993, and Peterson and Hollot, 1988). The uncertainty structure here allows time variations in the uncertain parameters and cross terms in the controlled output vector. These terms arise naturally in many practical problems, such as structural control in earthquake applications. The effects of sensor noise are also included. In particular, the authors develop sufficient conditions under which full recovery is possible in the presence of sensor noise. All results have elementary proofs, based on the bounded real lemma and standard Lyapunov stability theory. The relationship to control design with linear matrix inequalities is also discussed