Positiveness and Finite-Time Control of Dual-Switching Poisson Jump Networked Control Systems With Time-Varying Delays and Packet Drops

This article studies the stochastically finite-time
$L_{2}$
control problem for the time-varying delay positive dual-switching Poisson jump networked control systems (TVD-PDSPJ-NCSs) with packet drops. A key issue is that the TVD-PDSPJ-NCSs do not specify the jumping sequence of working processing modes. First, the TVD-PDSPJ-NCSs are modeled for the first time by considering the non-negative total amount of data, work processing modes jumping, and data transmission channel switching of the NCSs. Then, a proper finite-time state feedback controller is designed for the TVD-PDSPJ-NCSs so that the closed-loop dual-switching Poisson jump NCSs are positive, stochastically finite-time bounded, and fulfill the specified
$L_{2}$
disturbance attenuation performance simultaneously. By means of stochastic Lyapunov–Krasovskii functional methods, some sufficient conditions in the form of linear matrix inequalities are derived to obtain the finite-time state feedback controller gain. Furthermore, the optimal solution of the switching law is obtained such that the regulator can select the optimal data transmission channel according to the degree of packet drops. Finally, an application example is given to show the feasibility and validity of the proposed results.