A matrix sign function framework for robust stability analysis and parameter-dependent Lyapunov and Riccati equalities

This paper presents a new framework to deal with robust stability analysis for time-invariant parameter-dependent systems. It hinges upon two results: -the matrix sign function integral definition. -A particular representation of parameter-dependent matrices with negative and positive power series with respect to parameters. Exact solutions to parameter-dependent Lyapunov and Riccati equalities are derived. Several didactic examples are given throughout the paper to prove the validity of the proposed results.