STABILITY ANALYSIS BY PIECEWISE AFFINE APPROXIMATIONS AND PWL LYAPUNOV FUNCTIONS

摘要

In this paper we study the problem of analysis of nonlinear dynamics by piecewise affine approximations and piecewise linear (PWL) Lyapunov functions. We report results of numerical investigations of the quality of piecewise affine approximation. There is a need for such investigations since all available results concerning piecewise affine approximations are rather intuitive. We derive expressions for directional derivatives of the PWL Lyapunov function along trajectories of the piecewise affine system. We derive stability and instability conditions for the equilibrium point in the form of systems of linear inequalities, similar to those in [14] and [16]. Such systems can be solved by using linear programming (LP) solvers which make the proposed method numerically tractable. Finally we show numerical examples of computing stability regions and proving instability of equilibria with the use of our method.