In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

In this article, for Itô stochastic systems with aperiodic sampling and multiple time-delays, we provide two different types of mean square exponential stability analysis methods. One method is based on the Razumikhin-type theorems method, based on this method, the mean square exponential stability criteria of the system are proposed. Meanwhile, mean square exponential practical stability criteria are also proposed. In addition, through these theorems, the constraint of positivity on the Lyapunov function for all times can be relaxed to sampling times for Itô stochastic systems with aperiodic sampling and multiple time-delays is proved. Another method is based on the looped-functionals method. Two looped-functionals are introduced to analyze the stability of Itô stochastic systems with aperiodic sampling and multiple time-delays. One functional is one-sided, while the other functional is two-sided. Based on these two functionals and the Itô formula, two mean square exponential stability criteria are presented in the form of linear matrix inequalities. Numerical examples are used to illustrate that the proposed approach is less conservative than other methods.

In this paper, the dissipativity-based sampled-data control problem is studied for fuzzy switched Markovian jump systems (FSMJS). By considering the problem of the asynchronous switching caused by the subsystems switching occurred during the sampling intervals, constructing novel time-dependent Lyapunov functional, and using average dwell time (ADT) approach, sufficient mean-square exponential stability criteria and strictly $(\mathcal{Q,S,R}) - \gamma -$ dissipativity criteria are proposed under the constraints on that the maximum sampling period is no larger than the dwell-time between the transition rates switching instants. Meanwhile, a relationship between ADT and sampling period is revealed for FSMJS. Based on the strictly $(\mathcal{Q,S,R}) - \gamma -$ dissipativity criteria, the sampled-data controller is designed for FSMJSs. A circuit simulation example is provided to illustrate the effectiveness of the proposed method.

In this article, an aperiodic sampled-data control problem is investigated for polytopic uncertain switched complex dynamical networks subject to actuator saturation. Due to the constraint on the upper bound of the sampling interval being no greater than the dwell time, the issue concerning the asynchronization between the sampled-data controller mode and the system mode is hence considered to be caused by subsystems that may switch in a sampling interval. By considering the sampling interval without switching and the sampling interval with switching, the parameters-dependent loop-based Lyapunov functionals are constructed, respectively. With the help of the constructed functional, mean-square exponential stability criteria for the error polytopic uncertain switched complex dynamical networks are presented under the definition of average dwell time. Furthermore, based on the stability criteria, the asynchronous aperiodic sampled-data controller is designed for polytopic uncertain switched complex dynamical networks subject to actuator saturation. The polytopic uncertain switched complex dynamical networks can be guaranteed to exponentially synchronize with the target node based on the proposed stability conditions and aperiodic sampled-data controller design method. Finally, by transforming the proposed theoretical conditions into the LMI-based objective optimization problem, the domain of attraction of polytopic uncertain switched complex dynamical networks is estimated. An example based on switched Chua’s circuit is applied to verify the effectiveness of the proposed method.

The issue of adaptive output-feedback stabilization is investigated for a category of stochastic nonstrict-feedback nonlinear systems subject to unmeasured state and unknown control directions. By combining the event-triggered mechanism and backstepping technology, an adaptive fuzzy output-feedback controller is devised. In order to make the controller design feasible, a linear state transformation is introduced into the initial system. At the same time, the Nussbaum function technology is used to overcome the difficulties caused by unknown control directions, and the state observer solves the problem of the unmeasured state. Based on the fuzzy-logic system and its structural characteristics, the issue of unknown nonlinear function with nonstrict-feedback structure in the system is tackled. The designed controller could not only guarantee all signals of closed-loop systems are bounded in probability but also save communication resources effectively. Finally, numerical simulation and ship dynamics example are given to confirm the effectiveness of the proposed method.