Robustness analysis of uncertain linear descriptor systems: Unified approaches using gLFTs, LMIs, and μ

This paper studies the impulsive behavior and robust stability and performance of continuous-time uncertain linear descriptor systems, which are described by a combination of differential and algebraic equations. We present necessary and sufficient conditions for robust stability and several dissipation performance indices of uncertain linear descriptor systems represented as generalized linear fractional transformations (gLFTs). The conditions are written as linear matrix inequalities (LMIs), which are computable in polynomial-time. Unified and generalizable convex conditions are provided for the analysis of robust stability and performance for linear descriptor systems with structured uncertainty. A necessary and sufficient condition for robust impulse-free dynamics for structured uncertain systems is derived from using structured singular value (μ) theory and incorporated into associated robust stability conditions.