An approximate stability analysis of nonlinear systems described by Universal Learning Networks

Stability is one of the most important subjects in control systems. As for the stability of nonlinear dynamical systems, Lyapunov’s direct method and linearized stability analysis method have been widely used. But, it is generally recognized that finding an appropriate Lyapunov function is fairly difficult especially for the nonlinear dynamical systems, and also it is not so easy for the linearized stability analysis to find the locally asymptotically stable region. Therefore, it is crucial and highly motivated to develop a new stability analysis method, which is easy to use and can easily study the locally asymptotically stable region at least approximately, if not exactly. On the other hand, as for the calculation of the higher order derivative, Universal Learning Networks (ULNs) are equipped with a systematic mechanism that calculates their first and second order derivatives exactly. So, in this paper, an approximate stability analysis method based on h approximation is propo...

• Type: Journal
• Year: 2007
• Where: ASC
• Authors: Kotaro Hirasawa, Shingo Mabu, Shinji Eto, Jinglu Hu
• Keywords: ASC 2006, ASC 2007, Nonlinear Dynamical Systems, Stability Analysis, Stability Analysis Method