Observer feedback for uncertain systems

In this study feedback design procedures are developed for linear multivariable systems with uncertain parameters and inaccessible states. An observer is used in the feedback loop. The basic design parameters are the observer gain matrix and the state-estimate feed-back matrix. Two models of uncertainty are considered. One is a "deterministic" model where the parameters are assumed to vary within specified bounds. The other is a "random" model where the parameters are assumed to have white noise random variations. The prime design objective is to reduce as much as possible an integral-quadratic performance measure. In the random case the expected value of the integral-quadratic form is used for minimization while in the deterministic case an upper bound on the integral-quadratic is used. Gradients are used to compute the "optimal" design parameters. The required gradients are computed from the solution of Lyapunov equations.