Robustness of suboptimal control: Gain and phase margin

The purpose of this paper is to introduce the gain and phase margin as measures of robustness of suboptimal linear-quadratic regulators. It will be shown that the suboptimal control retains the infinite gain margin of the corresponding optimal system, but that the phase margin and gain reduction tolerance depend on the degree of suboptimality of the nominal optimal control law. This establishes the degree of suboptimality as an index of both the system performance regarding the optimality criterion and the robustness to plant parameter uncertainties and distortions of the optimal control law. It will also be shown that the suboptimal closed-loop systems remain stable despite insertion of memoryless nonlinear gains inside individual feedback loops, thus raising further the confidence in suboptimal designs of linear-quadratic regulators.