An LMI formulation of robustness analysis for systems with time-varying and LTI uncertainty

Abstract

Abstract : A procedure is developed to analyze uncertain systems having both time varying (TV) and linear, time-invariant (LTI) uncertainty. The problem is formulated as a two step procedure involving the solution of two sets of LMIs using both constant and frequency dependent scales to account for the different types of uncertainty. In the first step, the scales corresponding to the TV parameters are constrained to be constant over a set of frequencies and both constant and frequency dependent scales are computed to minimize the peak value of the robustness bound for the chosen frequencies. In the second step, the constant scales are held fixed and the frequency dependent scales corresponding to the LTI uncertainty are computed to minimize the robust ness bound at each frequency. Numerical examples are given to demonstrate the procedure, which gives a less conservative result than previously shown and thus allows for more accurate analysis of systems with TV and LTI uncertainty.