Xingwen LiuProfessor, chair of the School of Electrical Engineering, Southwest Minzu University, China
Speech Title: Convergence of Perturbed Delayed Switched Nonlinear Systems with Applications
Abstract: Switched delayed nonlinear systems are a typical class of complex systems and have wide applications. This talk will reveal the following properties of switched delayed nonlinear systems subject to perturbations: (i) Suppose that the nominal system is exponentially stable. Then the trajectories of perturbed system decay exponentially if so is the perturbation, and decay asymptotically if so is the perturbation. The conclusions hold for both local and global cases. (ii) Suppose that the nominal system is asymptotically stable. Then the trajectories of perturbed system decay asymptotically to zero if the perturbation decays to zero exponentially, and may diverge if the perturbation asymptotically decays to zero. Utilizing these properties, some important stability conditions can be established: Suppose that a cascade switched nonlinear delayed system consists of two separate systems and that the coupling term satisfies a linear growth rate condition. Then the cascade system is exponentially stable, locally or globally, if and only if so are two separate systems and is locally asymptotically stable if one of separate systems is locally asymptotically stable and the other one is locally exponentially stable.
Biography: Dr. Xingwen Liu is a professor and chair of the School of Electrical Engineering, Southwest Minzu University. His main research interest is control theory and engineering, including complex systems, robust control, and game theory. He has established some fundamental results in this filed, for example, fully characterizing the asymptotic stability of delayed positive systems and the exponential stability of cascade switched nonlinear systems with delays. Prof. Liu served as a general co-chair of the 6th International Conference on Positive Systems, and is on the editorial boards of Mathematical Modelling and Control, the Journal of Engineering and Technology Research.