Mode-Independent Stabilization of Markovian Jump Systems With Time-Varying Delays: A Sliding Mode Approach

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Ran Huang ◽  
Yan Lin ◽  
Zhongwei Lin
Keyword(s):  
Closed Loop ◽  
Sliding Mode ◽  
Markovian Jump Systems ◽  
Time Varying ◽  
Sliding Surface ◽  
Closed Loop System ◽  
Markovian Jump ◽  
Detection Function ◽  
Jump Systems ◽  
Real Plant

This paper investigates mode-independent stabilization of Markovian jump systems with time-varying delays via a sliding mode approach. A sufficient condition is proposed to guarantee the existence of a mode-independent sliding surface. Because the real plant regime mode is not directly accessible and instantly available, a controller is reconfigured online by calculating a detection function such that the closed-loop system converges to the sliding surface in finite time. A comparison example is presented to illustrate merits of the developed theory.

scholarly journals Finite-TimeH∞Filtering for Singular Stochastic Markovian Jump Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Yan ◽  
Xiaojia Zhou ◽  
Jun Cheng ◽  
Fangnian Lang
Keyword(s):  
Finite Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Time Interval ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Finite Time Boundedness ◽  
Jump Systems

The issue of finite-timeH∞filtering for singular stochastic Markovian jump systems with time-varying delays is concerned in this paper.H∞filtering is designed for underlying closed-loop singular Markovian jump system and system state does not exceed a given bound over some finite-time interval. Considering the full information of underlying Markov process, sufficient conditions are obtained to guarantee that the described system is finite-time stability andH∞filtering finite-time boundedness. By establishing the results of stochastic character and finite-time boundedness, the closed-loop singular Markovian jump system trajectory stays within the given bound. At last, a numerical example is supplied to show the efficiency of the proposed method.

scholarly journals Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

Machines ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 259
Author(s):  
Min Cheng ◽  
Chunyang Zhang ◽  
Jin Qiu ◽  
Zhengtian Wu ◽  
Qing Gao
Keyword(s):  
Sliding Mode ◽  
Fuzzy Model ◽  
Observer Design ◽  
Markovian Jump Systems ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Luenberger Observer ◽  
Jump Systems ◽  
Sliding Mode Dynamics ◽  
Event Triggered

This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an H∞ attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method.

scholarly journals Observer-Based Sliding Mode Control for Stochastic Nonlinear Markovian Jump Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Xiaohan Yin ◽  
Quanxin Zhu
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Markovian Jump Systems ◽  
Control Law ◽  
Closed Loop System ◽  
Markovian Jump ◽  
Mode Control ◽  
Disturbance Term ◽  
Jump Systems ◽  
Nonlinear Markovian Jump Systems

We consider a class of stochastic nonlinear Markovian jump systems (MJSs) with partly unknown transition rate and time-varying delays. The system under consideration is subject to the mode uncertainties and nonlinear term and disturbance term which are unknown. The main mission is to design the observer-based sliding mode controller for such a complex system. An observer is first constructed, and then we design an integral sliding mode surface such that the MJSs satisfy the reaching condition. The sliding mode control law ensures the stochastic stability of the closed-loop system. Finally, an example is given to illustrate the proposed results.

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