Analysis of LPV systems using a piecewise affine parameter-dependent Lyapunov function

This paper presents new finite-dimensional linear matrix inequality (LMI) formulations for the stability and induced L₂ performance analysis of linear parameter-varying (LPV) systems. The approach is based on the nonsmooth, dissipative system theory using a continuous, piecewise affine parameter-dependent Lyapunov function (PAPDLF). The new method is shown to be less conservative than previously published techniques that are based on either affine parameter-dependent Lyapunov functions or robust control techniques. Conservatism is reduced with this new approach because the analysis is performed over several, smaller subregions of the parameter space rather than the entire region. The new analysis approach also uses a more general class of parameter-dependent Lyapunov functions. In contrast to the gridding approach typically used to develop a computationally feasible algorithm, this proposed approach guarantees the analysis result. While computationally intensive, we show that the numerical results using our approach can be used to develop many new insights into the potential conservatism of various classes of Lyapunov functions for LPV systems