Guaranteed Dwell-Times of Hysteresis Switching for Switched Nonlinear Systems via Switching Characteristic Indices

This paper studies the challenging issue of how to guarantee dwell-times of a state-dependent hysteresis switching law for switched nonlinear systems. The classical convex combination condition is utilized to construct buffer-regions. In the buffer-regions, by virtue of Lie derivative of the induced single Lyapunov function along the active vector field, the position of state at the switching instant and the evolution of state during the active interval are captured in a uniformly quantitative form via switching characteristic indices for the first time. These uniform indices are revealed as the essential attribute by which the dwell-times of hysteresis switching are guaranteed. Meanwhile, the dwell-times are associated with subsystems and can be adjusted by an introduced parameter, which ensures the adjustable multiple dwell-times for every subsystem, rather than one dwell-time for the whole systems. Moreover, for switched linear systems, the explicit expression of multiple dwell-times is obtained by using the convex condition with respect to system matrices and independent of dwell-times. A numerical example substantiates the effectiveness.