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This paper studies the robust finite-time energy-to-peak filtering problem for a class of uncertain nonlinear Markovian jumping systems (MJSs) with energy constraint external disturbances. The Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear MJSs. By selecting the appropriate Lyapunov–Krasovskii functional, a sufficient condition is derived such that the filtering error dynamic fuzzy MJSs are finite-time stable and have a prescribed level of L 2 – L ∞ disturbance attenuation in a finite time-interval. The sufficient condition on the existence of robust finite-time energy-to-peak fuzzy filtering criterion is formulated in the form of linear matrix inequalities and the designed finite-time energy-to-peak fuzzy filter is described as an optimization one. A numerical example is given to illustrate the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of non-fragile observer-based passive control for a class of Markovian jumping systems (MJSs) subjected to uncertainties, nonlinearities and time-delays. Based on the Takagi–Sugeno fuzzy models, the dynamics of mode-dependent non-fragile state observer and feedback controller system and the combined closed-loop fuzzy dynamic MJSs are constructed. A sufficient condition for passivity and stochastic stability of the combined system is derived and proved by means of the Lyapunov–Krasovskii functional methods and linear matrix inequalities (LMIs) techniques. The non-fragile passive controller and observer parameters can be solved directly by using the existing LMIs optimization techniques. Finally, a numerical simulation is given to illustrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: The unbiased H ∞ filtering problem is considered for a class of Markov jump systems (MJSs) with distributed time-delays. Based on the selected Lyapunov–Krasovskii functional, it gives a sufficient condition for the existence of the mode-dependent unbiased H ∞ filter such that the filtering error dynamic MJSs is stochastically stable and satisfies a prescribed level of H ∞ disturbance attenuation in an infinite time-interval. The design criterions are presented in the form of linear matrix inequality techniques, and then are described as the optimization problems. At last, two numerical examples are employed to illustrate the effectiveness of the developed techniques. [Copyright &y& Elsevier]

Abstract: The stochastic finite-time boundedness (FTB) problem is considered for a class of Markovian jumping neural networks (MJNNs) with time delay and uncertainties. By selecting the appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions of stochastic FTB of MJNNs are presented and proved. The FTB criteria are formulated in the form of linear matrix inequalities. Simulation results illustrate the effectiveness of the developed approaches. [Copyright &y& Elsevier]

Abstract: This paper studies the robust fault detection filter (RFDF) design problems for uncertain nonlinear Markov jump systems with state delays and parameter uncertainties. By means of Takagi–Sugeno fuzzy models, the dynamics of filtering error generator and the fuzzy RFDF system are constructed. With the aid of the selected weighting matrix function, the design objective is to find an optimal RFDF which results in a minimal difference between the reference model (ideal solution) and the RFDF (real solution) to be designed. A sufficient condition is firstly established on the stochastic stability by using stochastic Lyapunov–Krasovskii functional approach. Then in terms of linear matrix inequalities techniques, sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as an optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences. [Copyright &y& Elsevier]

Abstract: This paper studied the proportional-integral (PI) control problems of stochastic Markovian jump systems (MJSs) with uncertain parameters. Under complete access to the system states, the PI controller design procedure turns to static output feedback control problem that make the closed-loop dynamics of this class of uncertain MJSs be robustly stochastically stable. A sufficient condition on the existence of PI controller is presented and proved by means of linear matrix inequality techniques. The presented results are extended to the case when the system states are not accessible. In order to make the relative equations approximate with a satisfactory precision, we described the problem as a semidefinite programming one via disciplined convex optimization. Simulation results illustrate the validity of the proposed algorithms. [Copyright &y& Elsevier]

Abstract: The stochastic finite-time boundedness problem is considered for a class of uncertain Markovian jumping neural networks (MJNNs) that possess partially known transition jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By selecting the appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions of stochastic finite time boundedness of MJNNs are presented and proved. The boundedness criteria are formulated in the form of linear matrix inequalities and the designed algorithms are described as optimization ones. Simulation results illustrate the effectiveness of the developed approaches. [Copyright &y& Elsevier]

Abstract: This paper provides the observer-based finite-time control problem of time-delayed Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time H ∞ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches. [Copyright &y& Elsevier]

Abstract: The peak-to-peak filtering problem is studied for a class of Markov jump systems with uncertain parameters. By re-constructing the system, the dynamic filtering error system is obtained. The objective is to design a peak-to-peak filter such that the induced gain from the unknown inputs to the estimated errors is minimized or guaranteed to be less or equal to a prescribed value. By using appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions are initially established on the existence of mode-dependent peak-to-peak filter which also guarantees the stochastic stability of the filtering error dynamic systems. The design criterions are presented in the form of linear matrix inequalities and then described as an optimization problem. Simulation results demonstrate the validity of the proposed approaches. [Copyright &y& Elsevier]

• Fault detection scheme for conic nonlinear systems in finite frequency domain is designed. • Sufficient conditions to realize H_ fault sensitivity and H_ disturbance attenuation. • The fuzzy fault detection problem is transformed into an optimization algorithm. • A tunnel diode-circuit is given to confirm the validity of the designed scheme. In this paper, we focused on the issue of fault detection subject to a class of conic-type nonlinear systems in the finite frequency domain (FFD). Applying Takagi Sugeno (T-S) fuzzy models, the conic-type dynamic error system is established. To prove that the residual vector is robust to external disturbances and sensitive to faults, we provide some conditions to realize H − fault sensitivity performance and H ∞ disturbance attenuation performance within the FFD. Then, utilizing linear matrix inequalities techniques, the fuzzy fault detection observer design problem is transformed into an optimization algorithm. Finally, a numerical example related to a tunnel diode-circuit is given to confirm the validity of the designed scheme. [ABSTRACT FROM AUTHOR]

This paper addresses finite-time boundedness and stabilization problem for n -neuron uncertain positive Markovian jumping neural networks (MJNNs). Firstly, we analyze the positive MJNNs in the input-free case and then propose a sufficient condition to ensure the input-free finite-time boundedness. Then applying the state feedback scheme, a suitable finite-time stabilizable controller is devised to guarantee the positiveness of the closed-loop MJNNs. Moreover, some sufficient conditions for the existence of the controller gain solutions are proposed and proved by using the stochastic Lyapunov-Krasovskii functional approach and linear matrix inequalities techniques. Finally, we give two simulation examples to demonstrate the effectiveness and feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper addresses finite-region asynchronous H ∞ filtering for a class of two-dimensional Markov jump systems (2-D MJSs). A mathematical model is established using the Roesser model, and asynchrony is accounted for using a hidden Markov model (HMM). The modes jumping between the target system and the designed filter are determined by the given conditional probability matrix. Sufficient conditions are derived using suitable Lyapunov function and linear matrix inequalities (LMIs) to ensure stable filtering performance. The practical applicability of the approach is illustrated by two examples. Overall, this study offers a method to tackle filtering challenges in 2-D Markov jump systems, incorporating HMM, Lyapunov functions, and LMIs to effectively solve the finite-region asynchronous H ∞ filtering problem. • An HMM is used to describe the asynchronous phenomenon between the system and the filter. • Lyapunov functional and recursive formulas effectively analyze the FRB of filtering error system. • The Darboux equation and the heat exchange process both validate the effectiveness of the filter. [ABSTRACT FROM AUTHOR]

• An ETS is proposed to reduce energy consumption. • An event-triggered-based controller is designed for MJCPSs. • The uniform upper/lower bounds are used to describe DoS attacks. • Sufficient conditions are given to stabilize the MJCPSs. This paper is concerned with the event-triggered-based H ∞ control problem for Markov jump cyber-physical systems against denial-of-service attacks. The uniform upper and lower bounds are used to describe the characteristics of aperiodic denial-of-service attacks. An event-triggered scheme is introduced to reduce the waste of resources and avoid communication channel congestion. Based on multi-Lyapunov functions, sufficient conditions are proposed to guarantee the asymptotic mean-square stability and H ∞ performance of the switched closed-loop Markov jump cyber-physical systems. By solving linear matrix inequalities, the event-triggered-based controller gain matrices, and H ∞ performance index are obtained. In the simulation, an F-404 aircraft engine system is employed to clarify the validity of the proposed event-triggered-based controller design approach in face of denial-of-service attacks. [ABSTRACT FROM AUTHOR]

In this paper, we study the asynchronous observer-based sliding mode control for a class of discrete-time Markov jump systems with time-delay and conic-type nonlinearities. Firstly, we assume there exists a detector described by the hidden Markov model that provides estimated information of the system mode. Based on the detector, a common sliding surface and an observer-based controller are devised. Secondly, we select the appropriate Lyapunov functional and applying linear matrix inequalities techniques to get sufficient conditions such that the controller and observer gains are obtained, which can guarantee the stochastic stability and strict dissipativity of the sliding mode dynamics. Furthermore, the given H ∞ and passive performance are also discussed. Thirdly, to make the system trajectory get to the predetermined sliding surface, a sliding mode control law is proposed. Finally, an application related to the automotive electronic throttle body control system is given to illustrate the correctness and feasibility of this designed approach. [Display omitted] • For nonlinear MJSs, the observer-based asynchronous SMC scheme is designed. • For the reachability of the sliding surface, a SMC law is given. • By a practical example, the effectiveness of this designed approach is illustrated. [ABSTRACT FROM AUTHOR]