Robust Static H∞ Output-Feedback Control Using Polynomial Chaos

This article considers the H-infinity static output feedback control for linear time-invariant (LTI) uncertain systems with nonlinear dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos theory, the control synthesis problem is solved using a high-dimensional expanded system which characterizes stochastic state uncertainty propagation. In contrast to published polynomial chaos based control methods, the proposed approach aims at minimizing an upper bound of the L-2 gain from the disturbance to the controlled output. The effect of using a finite number of terms in the polynomial chaos expansions is captured by a time-varying norm-bounded uncertainty, and is explicitly taken into account. This feature avoids the use of high-order polynomial chaos expansions to alleviate the destabilizing effect of truncation errors, thus significantly reducing computational complexity. A numerical example illustrates the effectiveness of the proposed approach.