This work presents a computational approach for searching a Lyapunov function for the equilibrium point for a class of nonautonomous nonlinear systems , where is the state vector, is a possibly time-varying parameter vector, , and for all , is smooth. The Lyapunov function is considered in the form , where , are smooth basis-functions and are parameter matrices. The parameter matrices are sought from the condition, , where . The last condition is the condition of exponential stability of the equilibrium point.
The main contribution of this paper is the utilization of a flexible and general smooth parameterization of the Lyapunov function candidates that does not introduce significant conservativeness and the problem is reduced to a convex optimization problem involving linear inequality constraints at each point in the state space.