A computational method for determining quadratic lyapunov functions for non-linear systems

Authors:
E. J. Davison;E. M. Kurak
Affiliations:
Department of Electrical Engineering, University of Toronto, Canada;Department of Electrical Engineering, University of Toronto, Canada
Venue:
Automatica (Journal of IFAC)
Year:
1971

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Abstract

This paper deals with the problem of automatically constructing a quadratic Lyapunov Function V = x'Ax for a high order non-linear system given by x@? = f(x), f(0) = 0, where f(x) is a continuous function of x which guarantees uniqueness of solutions of the system. The Lyapunov Function is found by a direct search technique so that the volume of the asymptotic stability region obtained for the system, x'Ax = 1, is maximized, thereby giving an estimate of the asymptotic stability boundary of the system. Experimental results show that such a procedure gives an excellent approximation to the exact asymptotic stability region for a system. Numerical examples are included in the paper for second, third and fourth order systems.