On computational issues for stability analysis of LPV systems using parameter‐dependent Lyapunov functions and LMIs

Abstract

Summary Robust stability analysis of linear systems subject to time‐varying parameters is investigated. The objective is to discuss some computational issues associated with solving stability conditions based on parameter‐dependent Lyapunov functions by means of linear matrix inequalities (LMIs), which are exacerbated as the quantity of time‐varying parameters increases. A new solution related to the inclusion of the time derivatives of the parameters is proposed, improving the computational cost without resulting in much conservatism. The time complexity to solve the LMIs reduces from factorial to linear. Numerical examples are provide to illustrate the advantages of the proposed methodology.