Volatile Discrete-Time Observation Stabilization of Time-Varying Hybrid Stochastic Large-Scale Networks

This paper focuses on the exponential stability of time-varying hybrid stochastic large-scale networks, in which a novel discrete-time observation control strategy with volatile control gain is imposed. The control gain exhibits sign-indefinite characteristics that follow certain volatile patterns. Then, the strategy can preferably respond to extrinsic perturbances and defend actuators and facilities by comparison with the position in constant gain. To quantify the volatile control gain, a concept of average volatile discrete-time observation control gain is proposed. In light of stochastic analysis theory and Lyapunov method, we establish improved stability criteria. In contrast to earlier results, the piecewise continuous, time-varying, and indefinite functions replace the constant coefficient of the upper bound estimation for the operator of the Lyapunov function, i.e., it can be positive or negative along time evolution, which shows wider applications of our results. Furthermore, considering the phenomenon of controller failure and packet losses, obtained results are applicable for analyzing the stabilization via intermittent discrete-time observation control and nonuniform discrete-time observation control, respectively. Finally, two applications to oscillator systems and single-link robot arms are presented and numerical simulations are exploited to illustrate the feasibility. Note to Practitioners—This paper is motivated by existing results on discrete-time observation control for the dynamics of hybrid stochastic large-scale networks. The existing results mainly require continuous updates to the control signals while maintaining a constant control gain. This is challenging to achieve on digital computers and often does not effectively respond to external disturbances. This paper designs a new hybrid control called volatile discrete-time observation control, and a concept of the control gain is proposed to quantify the volatile control gain. Specifically, the obtained results also apply to scenarios involving control failures and packet loss. The results are applied to oscillator systems and single-link robot arms, demonstrating their effectiveness and it is expected that the proposed approach can be extended to more practical physical engineering systems.