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This article focuses on the finite-time asynchronous output feedback control scheme for a class of Markov jump systems subject to external disturbances and nonlinearities. The conic-type nonlinearities hold a constraint condition which locates in a known hyper-sphere with an indefinite center. In addition, the asynchronization phenomenon occurs between the system and the controller, which can be represented by means of a hidden Markov model. A sufficient condition is derived not only to guarantee the finite-time boundedness of the acquired closed-loop systems but also to possess a desired $H_{\infty }$ performance on the basis of Lyapunov functional technique. Finally, the validity and feasibility of the proposed method are demonstrated with a dc-motor experiment. [ABSTRACT FROM AUTHOR]

This article study the asynchronous control problem for a class of discrete-time Markovian jumping Lur’e systems (MJLSs) over the finite-time interval. The partial accessibility of system modes with respect to the designed controller is described by a hidden Markov model (HMM). The asynchronous control law consists of two parts, i.e., the states and the nonlinearities involved in the dynamics of the controlled system. By selecting the appropriate Lyapunov functional and applying the modified sector condition, the finite-time stabilization conditions under the control constraints are derived. Finally, the effectiveness of the designed method is verified by an illustrative simulation. [ABSTRACT FROM AUTHOR]

An observer‐based finite‐time asynchronous H∞ control law is designed for a class of hidden Markov jumping systems with non‐linearities and external disturbances. The non‐linearities satisfy the conic‐type constraint condition that lies in a known hypersphere with an uncertain centre. The non‐synchronisation phenomenon between the system modes and observer/controller modes is modelled by a hidden Markov model. By means of the proper stochastic Lyapunov–Krasovskii functional method, a sufficient condition is obtained to guarantee the stochastic finite‐time boundedness of the corresponding argument error dynamic systems with a satisfied H∞ disturbance rejection level. Finally, the feasibility and validity of the main results is illustrated through a pratical example related to the DC motor. [ABSTRACT FROM AUTHOR]

• The H ∞ fault-tolerant control scheme is studied for a class of conic-type nonlinear Markov jump systems with sensor and actuator faults. • The hidden Markov model is introduced to deal with the asynchronous phenomenon, and the H ∞ fault-tolerant controller is designed by selecting suitable Lyapunov-Krasovskii functional. • The proposed control strategy can not only ensure the finite-time boundedness of the closed-loop system, but also guarantee the required H ∞ performance. This paper studies the H ∞ fault-tolerant control problem for a class of conic-type nonlinear Markov jump systems with sensor and actuator faults as well as unknown disturbances. Firstly, the hidden Markov model is introduced to deal with the asynchronous problem existing in the control systems. By selecting suitable Lyapunov-Krasovskii function, linear matrix inequalities techniques are applied to obtain the H ∞ fault-tolerant controller. A new condition of the state feedback H ∞ fault-tolerant controller with actuator faults and sensor faults is presented. The proposed control strategy can not only ensure the finite-time boundness of the closed loop system, but also guarantee the required H ∞ performance. Lastly, the availability of the design scheme is validated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of the finite-region H ∞ asynchronous control scheme, which is devoted to the transient behavior of a class of two-dimensional Markov jump systems. The disquisitive system is characterized based upon a Roesser model. Considering the fact that there exists an asynchronous phenomenon between the controlled plant and the controller, we introduce a hidden Markov model to address the non-synchronization. By resorting to a given conditional probability matrix, the mode jumps between the controlled plant and the controller are determined. To conclude, an example is employed to illustrate the potential applications of the devised approach. [ABSTRACT FROM AUTHOR]

Based on the two-dimensional (2D) Roesser model, this paper focuses on the asynchronous controller design for directional 2D Markov jump systems (MJSs). Considering the more practical situation that the modes of the 2D MJSs in the horizontal and vertical directions are independent, and the system modes are asynchronous with that of the controller, the directional 2D MJSs are proposed and the asynchronous controller is designed, respectively. Based on the Lyapunov theory, a sufficient condition for the mean square exponential stability of the controlled directional 2D MJSs is given. Moreover, the partially unknown transition probabilities in systems and controllers are considered. Finally, an example is given to illustrate that the proposed method is effective. [ABSTRACT FROM AUTHOR]

This paper concerns the issue of finite-time dissipative asynchronous output feedback control for a wind turbine system that can be modelled as Markov jump Lur'e systems. Due to quantisation, time delays and ubiquitous data dropouts, the actual controller modes in practical application cannot always operate synchronously with the plant modes. To conquer this difficulty, a hidden Markov model is employed to provide some estimated modes information for controlling. In addition, by the Lyapunov function approach and linear matrix inequality technology, sufficient conditions are developed to guarantee finite-time boundedness of the continuous-time closed-loop system subject to strictly (U , G , V) -α-dissipative performance. Finally, a simulation example of a wind turbine system is given to verify the correctness and applicability of the proposed controller. [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]

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]

• Design an asynchronous fault detection filter for non-homogeneous MJSs. • The system modes can be traced by an asynchronous fault detection filter. • Sufficient conditions are devised to ensure the designed system performance. • The AETB is used to validate the devised asynchronous fault detection filter. This work investigates the asynchronous fault detection filtering issue for discrete-time piecewise homogeneous Markov jump systems. By resorting to a dual hidden Markov model, an asynchronous fault detection filter is presented which can follow up the system modes. Utilizing the stochastic Lyapunov function approach, sufficient conditions are devised to make the resultant Markov jump systems be stochastically stable and hold a specified H ∞ performance level. Finally, a real-time experiment based on the automotive electronic throttle body is employed to validate the devised asynchronous fault detection filter which can find the faults after the occurrences in the case of no false alarm. [ABSTRACT FROM AUTHOR]