Output tracking of Markovian jumping systems via error feedback regulation

This paper is concerned with the boundary error feedback regulation for a one-dimensional anti-stable wave equation with distributed disturbance generated by a finite-dimensional exogenous system. Transport equation and regulator equation are introduced first to deal with the anti-damping on boundary and the distributed disturbance of the original system. Then, the tracking error and its derivative are measured to design an observer for both exosystem and auxiliary partial differential equation (PDE) system to recover the state. After proving the well-posedness of the regulator equations, we propose an observer-based controller to regulate the tracking error to zero exponentially and keep the states of all the internal loop uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed controller.

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Sliding Mode Controller Design for Conic-Type Nonlinear Semi-Markovian Jumping Systems of Time-Delayed Chua's Circuit

IEEE Transactions on Systems Man and Cybernetics Systems ◽

10.1109/tsmc.2019.2914491 ◽

2019 ◽

pp. 1-9 ◽

Cited By ~ 8

Author(s):

Rong Nie ◽

Shuping He ◽

Fei Liu ◽

Xiaoli Luan

Keyword(s):

Controller Design ◽

Sliding Mode ◽

Sliding Mode Controller ◽

Chua’S Circuit ◽

Markovian Jumping ◽

Chua's Circuit ◽

Markovian Jumping Systems

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Stabilization of Fuzzy Markovian Jumping Systems with Distributed Delay

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.556-562.4386 ◽

2014 ◽

Vol 556-562 ◽

pp. 4386-4390

Author(s):

Zhao Ping Yuan

Keyword(s):

Time Delay ◽

Robust Stabilization ◽

Distributed Delay ◽

Lyapunov Stability Theory ◽

Linear Matrix ◽

Markovian Jumping ◽

Weighting Matrix ◽

Markovian Jumping Systems ◽

Distributed Time Delay ◽

Delay Dependent

This paper is concerned with the stabilization problem for fuzzy Markovian jumping systems with distributed time delay. First, fuzzy Markovian jumping systems with distributed time delay are peoposed. Second, a novel criterion of delay-dependent robust stabilization for fuzzy Markovian jumping systems is established in terms of linear matrix inequalities (LMIs) by using Lyapunov stability theory and free-weighting matrix method. When these LMIS are feasible, an explicit expression of a desired adjustable state feedback controller is given. Based on the obtained criterion, the introduced controller ensures the overall closed-loop system asymptotically stable in mean square sense for all admissible uncertainties and time delay.

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Finite-Time Passivity and Passification Design for Markovian Jumping Systems with Mode-Dependent Time-Varying Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2017/3256871 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Chao Ma

Keyword(s):

Finite Time ◽

Functional Method ◽

Linear Matrix ◽

Time Varying ◽

Markovian Jumping ◽

Markovian Jumping Systems ◽

The Mean ◽

Delay Dependent ◽

Passivity And Passification ◽

Theoretical Results

This paper investigates the finite-time passivity and passification design problem for a class of Markovian jumping systems with mode-dependent time-varying delays. By employing the Lyapunov-Krasovskii functional method, delay-dependent sufficient criteria are derived to ensure the mean-square stochastically finite-time passivity. Based on the established results, mode-dependent passification controller is further designed in terms of linear matrix inequalities, such that the prescribed passive performance index of the resulting closed-loop system can be satisfied. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results.

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