Stabilization of stochastic highly nonlinear coupled systems with non-random switching via delay feedback control

Abstract

In this paper, we address the problem of stabilization for stochastic highly nonlinear coupled systems with non-random switching via delay feedback control. Specifically, in the absence of linear growth condition, non-random switching signals are introduced for the first time into stochastic highly nonlinear coupled systems, which renders existing Markovian switching based methods inapplicable to this paper. To fill this gap, a new stochastic analysis method is introduced, and the existence and uniqueness of the solution for stochastic highly nonlinear coupled systems are obtained. Furthermore, the stochastic highly nonlinear coupled switching systems can achieve delay-dependent exponential stability, and a clear upper bound of the delay can be acquired by the proposed approach, which is different from Halanay-type differential inequalities. Finally, a numerical example is presented, and the theoretical results are applied to nonlinear RLC circuit model to illustrate the effectiveness of the obtained results.