This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given L₂ performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka-Volterra population model is used to show the feasibility and validity of the main results.

This paper investigates the asynchronous resilient controller design problem for a class of nonlinear switched systems with time-delays and uncertainties in a given finite-time interval. By constructing proper multiple Lyapunov-Krasovskii functions and applying average dwell time methods, a switching law and the relevant asynchronous resilient controller are designed to guarantee the finite-time boundedness of the closed-loop system with a specified H ∞ performance index. The H ∞ resilient controller design problems can be derived by solving a set of linear matrix inequalities. A practical example is employed to demonstrate the availability of the proposed methods.

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.