Global Finite-Time Stabilization Of A Class Of Switched Nonlinear Systems In Lower Triangular Form

As an important class of hybrid dynamical systems, switched systems have become a hot topic due to the significance both in theory and applications. A class of switched nonlinear systems in lower triangular form has attracted a lot of attention in the recent years. It is worth pointing out that although some results on global stabilization under arbitrary switchings for the studied switched systems in some paper have been reported by backstepping, to the authors’best knowledge, no results are available in literatures on finite-time stabilization for such systems. This paper is concerned with the global finite-time stabilization problem for such a class of switched nonlinear systems under arbitrary switchings. This paper aims at solving this problem. The results will be summarized as follows:(1) In the third chapter, we investigate the global finite-time stabilization problem for a class of switched nonlinear systems in lower triangular form under arbitrary switchings. Based on adding one power integrator technique, both a class of continuous state feedback controller and a common Lyapunov function are simultaneously constructed such that the closed-loop switched system is global finite-time stability under arbitrary switchings. We introduce a continuous stabilization function instead of a smooth function. In the controller design process, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformation for each subsystem. An example has been employed to show the effectiveness of the proposed finite-time control design method.(2) In the fourth chapter, we investigate the global finite-time stabilization problem for a class of uncertainties switched nonlinear systems in lower triangular form under arbitrary switchings. Compared with the third chapter, the systems are more general and we present a new method that may achieve accelerated convergence speed and reduced settling time. Finally, an application example verifies the feasibility and effectiveness of the proposed finite-time control design method.