Lyapunov stability for continuous-time 2D nonlinear systems

This paper deals with the stability of continuous-time 2D nonlinear systems in the Roesser form. The concepts from 1D Lyapunov stability theory are extended to 2D nonlinear systems. To check the stability a direct Lyapunov method is developed. While the direct Lyapunov method has been recently proposed for discrete-time 2D nonlinear systems, to the best of our knowledge what proposed in this paper are the first results of this kind on stability of continuous-time 2D nonlinear systems. Analogous to 1D systems, a sufficient condition for the stability is the existence of a certain type of the Lyapunov function. A new technique for constructing Lyapunov functions for 2D nonlinear systems is proposed. The proposed method is based on the sum of squares decomposition, therefore it formulates the Lyapunov function search algorithmically. In this way polynomial nonlinearities can be handled exactly and a large class of other nonlinearities can be treated introducing some auxiliary variables and constrains.