Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria
- 254 Downloads
This paper studies the practical exponential set stabilization problem for switched nonlinear systems via a \(\tau \)-persistent approach. In these kinds of switched systems, every autonomous subsystem has one unique equilibrium point and these subsystems’ equilibria are different each other. Based on previous stability results of switched systems and a set of Gronwall–Bellman inequalities, we prove that the switched nonlinear system will reach the neighborhood of the corresponding subsystem equilibrium at every switching time. In addition, we constructively design a suitable \(\tau \)-persistent switching law to practically exponentially set stabilize the switched system. Finally, a numerical example is presented to illustrate the obtained results.
Keywords\(\varepsilon \)-Practical set stability Switched nonlinear systems \(\tau \)-Persistent switching law
This work was partially supported by the NSFC under Grants 11171079 and 11371371, the ARC Discovery Projects, Natural Science Foundation of Hubei Province of China (2014CFB141), HUST Independent Innovation Research Fund (GF and Natural Science).
- 8.Zhai, G., Michel, A.N.: On practical stability of switched systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, pp. 3488–3493, Las Vegas, Nevada, USA (2002)Google Scholar
- 9.Zhang, G., Han, C., Guan, Y., Wu, L.: Exponential stability analysis and stabilization of discrete-time nonlinear switched systems with time delays. Int. J. Innov. Comput. Inf. Control 8, 1973–1986 (2012)Google Scholar