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

✍ Scribed by E.J. Davison; E.M. Kurak

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 703 KB
• Volume: 7
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(71)90027-6

✦ Synopsis

A numerical method may be used to obtain a quadratic Lyapunov Function for a high order system x= f(x), where f(x) is a continuous function of x, so that the vohtme of the asymptotic stability reagion obtained is maximised.

Summary--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 k =fix), 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.