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In this paper, the state estimation problem for singularly perturbed switched complex dynamic networks (CDNs) is addressed, in which the persistent dwell-time (DT) switching mechanism is employed to depict the switchings among parameters of each node. In the aforementioned switching mechanism, the concept of stage consisting of the persistent portion and the DT portion is introduced. Based on the singular perturbation theory, a two-time-scaling variables containing fast and slow states are taken into account on the CDNs simultaneously, which make the constructed networks more realistic. Furthermore, the main aim is to design a mode-dependent estimator to track the state information that cannot be directly obtained and further ensures the global uniform exponential stability of the investigated systems with a generalized dissipativity property. Some sufficient criteria on the existence of the desired mode-dependent state estimator are established by utilizing a modified matrix decoupling method. Finally, the availability of the estimator design procedures is verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper is concerned with the nonfragile ${\mathcal {H}_{\infty }}$ control problem for discrete-time fast sampling Markovian jump singularly perturbed nonlinear systems described by the Takagi-Sugeno fuzzy model. By utilizing singular perturbation theory, a singular perturbation parameter (SPP) independent, i.e., ${\epsilon }$ -independent, condition is derived to make sure the underlying closed-loop system’s stability and a mixed $ {\mathcal {H}_{\infty }}$ and passive performance ${\gamma }$ , simultaneously. The ill-conditioned case caused by SPP could be eliminated on the basis of such a condition. With the aid of the stochastic analysis approach, the desired controller gains can be obtained, where the nonfragile property is fully considered to improve the tolerance of controller. Furthermore, a technique is developed to estimate the upper bound of SPP $\boldsymbol {\epsilon }$ in this paper by employing a useful inequality. The availability and practicability of the proposed design method are finally explained via a practical example of a tunnel diode circuit with a modified model and a numerical example. [ABSTRACT FROM AUTHOR]

This paper is devoted to the finite-time cluster synchronization issue of nonlinearly coupled complex networks which consist of discontinuous Lur’e systems. On the basis of the definition of Filippov regularization process and the measurable selection theorem, the discontinuously nonlinear function is mapped into a function-valued set, then a measurable function is accordingly selected from the Filippov set to ensure the existence of the solution for the discontinuous system. By designing the finite-time pinning controller, some sufficient conditions are obtained for cluster synchronization of the identical and nonidentical Lur’e networks, respectively. In addition, the settling time for achieving the cluster synchronization is estimated by applying the finite-time stability theory. And finally, a numerical example is presented to illustrate the validity of theoretical analysis. [ABSTRACT FROM AUTHOR]

This article aims at designing a dynamic event-triggered $\mathcal {H}_{\infty }$ load frequency controller for multi-area power systems affected by false data-injection attacks and denial-of-service attacks. A dynamic event-triggered scheme, whose threshold parameter varies with objective system states, is employed to make rational use of limited network bandwidth resources and improve the efficiency of the data utilization. Then, taking the impacts of the aforementioned hybrid cyber attacks into consideration, an attractive system model is established. Whereafter, several sufficient conditions, which can guarantee the exponential mean-square stability with a preset $\mathcal {H} _{\infty }$ performance index of the studied system, are obtained through utilizing Lyapunov stability theory. Additionally, the desired controller is designed via handling convex optimization problems. Finally, a simulation example is displayed to explain the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ filter design for linear stochastic time-varying delay systems based on the filter velocity constraint is considered in this dissertation. Different from existing $\mathcal {L}_{2}\,-\,\mathcal {L}_{\infty }$ performance analysis and filter design, a new criterion is proposed to make a more accurate judgment, which can not only guarantee the stability of the filtering error system with $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ performance level but also can estimate the convergence speed of the filter. The ideal filter should has the same convergence speed as the original system, so as to ensure the rapid convergence of the error system, but also not to reduce the anti-interference ability and increase the bandwidth of the filter system. By the new filter design method, an ideal filter can be designed, which can regulate the convergence speed of the filter system to the desired effect. A simulation instance is provided to exhibit the validity of the new approach. [ABSTRACT FROM AUTHOR]

The $\mathcal {H}_{\infty }$ state estimation issue for switched delayed inertial neural networks is addressed in this work. A more universal switching law, persistent dwell-time (DT) switching law, is considered here rather than average DT one of which switching frequency among subsystems is strictly limited, or DT one. Concurrently, time delays are inevitable when transmitting information, then taking the time-varying delays into account makes the constructed systems conform well with the actual situations. The main goal in the work is devoted to designing a state estimator to ensure that the state estimation error system is globally uniformly exponentially stable and satisfies a prescribed $\mathcal {H}_{\infty }$ noise attenuation level. A mixed time/mode-dependent Lyapunov–Krasovskii functional matched with the foregoing switching law is introduced. Through utilizing some reasonable inequalities and common matrix operations, some sufficient criteria which guarantee the aforesaid stability and the solvability of the addressed issue are presented. Finally, an illustrative example is provided to present the potentiality and validity of the developed results. [ABSTRACT FROM AUTHOR]

This article develops a generalized $\mathcal {H}$ -representation, which can transforms stochastic systems into deterministic systems. With the help of this new approach, the necessary and sufficient conditions of $p$ th moment asymptotic stability and stabilization of linear stochastic systems are addressed. Meanwhile, the generalized $\mathcal {H}$ -representation method is also applied to investigate $p$ th moment observability and $p$ th moment complete observability for the addressed systems. [ABSTRACT FROM AUTHOR]