General stabilization of non-autonomous hybrid systems with delays and random noises via delayed feedback control

Abstract

The feedback control, derived from delayed state observations, was triumphantly imported to H∞ and exponentially stabilize an unstable nonlinear hybrid system with time-invariant delay and random noise, which is adapt to autonomous systems. Spontaneously, given an unstable non-autonomous hybrid system with time-dependent delay and random noise, can one import a feedback control, derived from delayed state and mode observations, to stabilize it? Fortunately, this will be well done by the approach of multiple Lyapunov functionals. Surprisingly, it is revealed that the stabilization can be achieved not only in the forms of H∞ stability and exponential speed but also of polynomial speed and general speed. Furthermore, the interesting result with respect to polynomial growth at most is as well yielded here.