The gradient method of designing Lyapunov functions in problems of absolute stability

A new iterative algorithm is proposed for design Lyapunov functions from a range of quadratic forms for the problem of absolute stability. Continuous and digital systems with several nonstationary nonlinearities are considered. Lyapunov functions are Resigned by finding the saddle points of a certain, non-convex-concave, function. The algorithm is a gradient procedure of search for saddle points. For any initial approximation both the continuous and digital varieties of the algorithm are proved to converge.