Computer generated Lyapunov functions for a class of nonlinear systems

The problem of constructing Lyapunov functions for a class of nonlinear dynamical systems is considered. The problem is reduced to the construction of a polytope satisfying some conditions. A generalization of the concept of sector condition that it makes possible to evaluate a given nonlinear function by using a set of piecewise-linear functions is proposed. This improvement greatly reduces the conservatism in the stability analysis of nonlinear systems. Two algorithms for constructing such polytopes are proposed, and two examples are shown to demonstrate the usefulness of the results.<
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