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In this article, an extended state observer‐based finite‐region control scheme is presented for two‐dimensional Markov jump systems with unknown mismatched disturbances. The mathematical model of the two‐dimensional Markov jump systems is built on the well‐known Roesser model. By establishing special recursive formulas and utilizing the 2‐D Lyapunov function theory, sufficient conditions are obtained, which prove that the resultant system is finite‐region bounded, if some linear matrix inequalities are achieved. Then, we provide an algorithm to solve the extended state observer‐based controller gains. With the proposed control scheme, the external disturbances can be actively rejected from the system outputs. To conclude, a numerical example based on the Darboux equation is provided to demonstrate the validity and effectiveness of the devised control scheme. [ABSTRACT FROM AUTHOR]

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]

This paper is concerned with the sliding mode control (SMC) via finite-time stabilization (FTS) for a class of conic-type nonlinear semi-Markovian jumping systems (SMJSs). Comparing with the classical Markovian jumping systems, the transition rates of SMJSs are related to the random sojourn-time $g$. Based on this, a suitable SMC law for driving the state trajectories to the designed sliding surface within a finite-time interval is given. Then, the FTS over reaching phase and sliding motion phase is further proved to guarantee the FTS of the whole SMJSs. Finally, the effectiveness of the proposed method is demonstrated by a time-delayed Chua’s circuit simulation. [ABSTRACT FROM AUTHOR]

The finite‐time stabilisation for a class of time‐delayed Markovian jumping systems with conic nonlinearities is studied. The authors aim to design a suitable control law to stabilise the closed‐loop system during a specified finite time. An appropriate Lyapunov–Krasovskii functional method is given to ensure the existence of finite‐time stabilisation controller and the relevant sufficient conditions have been formulated in the form of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

This studies the infinite horizon optimal control problem for a class of continuous‐time systems subjected to multiplicative noises and Markovian jumps by using a data‐driven policy iteration algorithm. The optimal control problem is equivalent to solve a stochastic coupled algebraic Riccatic equation (CARE). An off‐line iteration algorithm is first established to converge the solutions of the stochastic CARE, which is generalised from an implicit iterative algorithm. By applying subsystems transformation (ST) technique, the off‐line iterative algorithm is decoupled into N parallel Kleinman's iterative equations. To learn the solution of the stochastic CARE from N decomposed linear subsystems data, an ST‐based data‐driven policy iteration algorithm is proposed and the convergence is proved. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed two iterative algorithms. [ABSTRACT FROM AUTHOR]

This study studies the online adaptive optimal control problems for a class of continuous‐time Markov jump linear systems (MJLSs) based on a novel policy iteration algorithm. By utilising a new decoupling technique named subsystems transformation, the authors re‐construct the MJLSs and a set of new coupled systems composed of N subsystems are obtained. The online policy iteration algorithm was used to solve the coupled algebraic matrix Riccati equations with partial knowledge regarding to the system dynamics, and the relevant optimal controllers equivalent to the investigated MJLSs are designed. Moreover, the convergence of the novel policy iteration algorithm is also established. Finally, a simulation example is given to illustrate the effectiveness and applicability of the proposed 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]

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

This paper studies the adaptive fault estimation problems for stochastic Markovian jump systems (MJSs) with time delays. With the aid of the selected Lyapunov-Krasovskii functional, the adaptive fault estimation algorithm based on adaptive observer is proposed to enhance the rapidity and accuracy performance of fault estimation. A sufficient condition on the existence of adaptive observer is presented and proved by means of linear matrix inequalities techniques. The presented results are extended to multiple time-delayed MJSs. Simulation results illustrate that the validity of the proposed adaptive faults estimation algorithms. [ABSTRACT FROM AUTHOR]

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: 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]

This paper studies the robust stochastic stability problem for a class of Markov jump systems with norm bounded uncertain parameters and distributed time-delays. Integral inequality techniques together with Lyapunov-Krasovskii functional approach are employed to develop new delay-dependent sufficient conditions for stochastic stability. The main results are derived via linear matrix inequalities formulation. Simulation examples illustrate the effectiveness of the developed techniques. [ABSTRACT FROM AUTHOR]

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]

Abstract: The unbiased H ∞ filtering problem is studied for stochastic Markov jump system with constant and neutral time-delays. By re-constructing the system, the dynamic filtering error characteristics of unknown inputs and time-delays are obtained. A sufficient condition is initially established on the existence of mode-dependent unbiased H ∞ filter of constant time-delay system using stochastic Lyapunov–Krasovskii function. Then, the unbiased H ∞ filter is also designed for the jump system with constant and neutral time-delays. The design criterions are presented in the form of linear matrix inequality. Finally, the unbiased H ∞ filtering problems are described as optimization algorithms. Numerical examples illustrate the effectiveness of the developed techniques. [Copyright &y& Elsevier]

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]