An Integral-Type Multiple Lyapunov Functions Approach for Switched Nonlinear Systems

An integral-type multiple Lyapunov functions (MLFs) approach for switched nonlinear systems is set up for the first time, which gives a more general condition for analyzing the behavior of switched nonlinear systems since the Branicky's nonincreasing condition is no longer assumed and the generalized MLFs condition is a special case of the condition provided. Meanwhile, based on the integral-type MLFs approach, global stabilization for a class of switched nonlinear systems in p-normal form is achieved by constructing state-feedback controllers of subsystems and a proper switching law, where the solvability of the problem under study for individual subsystems is not assumed. Two examples are also provided to demonstrate the effectiveness of the proposed design method.