LPV system analysis with quadratic separator

This paper considers a class of linear systems with unknown slowly time-varying parameters, and proposes a method for analyzing its stability, using the quadratic separator as a basic tool for the analysis. First we show the connection between the frequency-dependent input/output scaling in the μ-analysis and the parameter-dependent Lyapunov functions, assuming that the uncertain parameters are constant. We then use this basic result to give computationally verifiable conditions for robust stability against time-varying parameters with arbitrarily slow variations