Robust Output Variances Constrained Controller Design

A performance robust controller design for systems with multiple output constraints and unstructured uncertainties is proposed. With system uncertainties and output variance constraints given a priori, this algorithm, starting with a stability robust controller obtained from singular H¿ control design, tunes the controller gain to satisfy the output constraints while maintains the stability robustness. This algorithm is based on a modified algebraic Riccati equation. The existence condition for a solution to this equation turns out to be a necessary and sufficient condition for the quadratic stability of the uncertain system. Furthermore, it provides an upperbound on the steady state covariance. A dual deterministic problem is also given which is mathematically equivalent to the stochastic problem.