The μ Method to Robust Stability Analysis

The robust stability of systems under both plant and controller perturbations is analyzed, with an emphasis on additivenorm-bounded perturbation. Choosing the interconnection matrix M makes Δ(s) block diagonal matrices and absorbing any matrix makes ‖Δ(s)‖∞<1, the problem can be recast into a small structured singular value (μ) problem. If 2S + F ≤ 3, μ(M) = infσ(DMD-1). In this paper, the main result is supωμ(M)=‖M‖∞, thus the structured singular value(μ) problem for robust stability of SISO systems subject to additive norm-bounded perturbation, can be recast into H∞ control problem. Moreover, robust stability of MIMO systems can be unified in the same framework.