Structured Singular Value and Applications: Analyzing the Effect of Linear Time-Invariant Uncertainty in Linear Systems

Abstract

This entry presents the most commonly used formulations of robust stability and robust H 1 performance for linear systems with highly structured, linear, time-invariant uncertainty. The structured singular value function () is specifically defined for this purpose, involving a problem-specific set, called the uncertainty set. With the uncertainty set chosen, is a real-valued function defined on complex matrices of a fixed dimension. A few key properties are easily derived from the definition and then applied to solve the robustness analysis problem. Computation of , which is required to implement the analysis tests, is difficult, so computable and refinable upper and lower bounds are derived.