Stabilization by delay feedback control for highly nonlinear switched stochastic systems with time delays

Abstract

This paper firstly discusses the existence and boundedness of unique global solution for highly nonlinear switched stochastic systems (SSSs) with time delays, where the switching signal is deterministic switching signal. Although the existence and boundedness of unique global solution can be obtained under local Lipschitz condition and Khasminskii‐type condition, highly nonlinear SSSs with time delays may not be stable. Therefore, a delay feedback control function can be designed for studying the stability of highly nonlinear SSSs with time delays, whose coefficients do not satisfy the linear growth condition. By using the Mathematical induction, Lyapunov function approach and the average dwell time method, H∞ stability and the pth moment exponential stability are studied for highly nonlinear SSSs with time delays. An explanatory example is given to illustrate the effectiveness of the main results.

control of stochastic networked control systems with time‐varying delays: The event‐triggered sampling case

“…Therefore, our article is the first work on this interesting topic. Finally, we will consider the stabilization problem of some discontinuous systems or impulsive systems and switching systems (e.g., see References 15‐22, 42‐47) via the event‐triggered sampling control method.…”

“…With respect to the stabilization problem of stochastic systems, the reader can refer to some related works (e.g., see References 15‐22 and references therein). However, it should be pointed out that the works in References 15‐17 were mainly concentrated on the continuous‐time state feedback control (CTSFC), whereas the results in References 18‐22 focused on the discrete‐time state feedback control (DTSFC).…”

“…With respect to the stabilization problem of stochastic systems, the reader can refer to some related works (e.g., see References 15‐22 and references therein). However, it should be pointed out that the works in References 15‐17 were mainly concentrated on the continuous‐time state feedback control (CTSFC), whereas the results in References 18‐22 focused on the discrete‐time state feedback control (DTSFC). Generally speaking, the DTSFC is less costly and maybe more effective than the CTSFC since the observations and decisions for the DTSFC is often not required to be done all the time and they are made just in certain discrete time.…”

“…The main contributions of this article can be generalized in the following four aspects. (1) Different from the methods used in References 15‐22, a novel event‐triggered feedback control (ETFC) differentiate from the traditional time‐triggered feedback control (e.g., see References 15‐22) is designed in this article. (2) Compared with many results on the ETFC for discrete‐time stochastic systems (e.g., see References 24‐28), our research is mainly focused on the case of continuous‐time stochastic systems (CTSSs).…”

Some Fixed‐Point Theorems on Generalized Cyclic Mappings in B‐Metric‐Like Spaces

“…e development of the theory of fixed points in generalized metric space is very significant. At the same time, it is beneficial to promote the study of stability of stochastic systems in [23][24][25][26][27][28][29][30] by applying our theory.…”