Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities

Automatica ◽  
2018 ◽  
Vol 89 ◽  
pp. 349-357 ◽  
Author(s):  
Haibin Sun ◽  
Yankai Li ◽  
Guangdeng Zong ◽  
Linlin Hou
Keyword(s):  
Transition Probabilities ◽  
Disturbance Attenuation ◽  
Markovian Jump ◽  
Markovian Jump System

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

scholarly journals Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Lianglin Xiong ◽  
Xiaobing Zhou ◽  
Jie Qiu ◽  
Jing Lei
Keyword(s):  
Partial Information ◽  
Transition Probabilities ◽  
Mixed Delays ◽  
Transition Rates ◽  
Neutral Systems ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Analysis Technique ◽  
Transition Rate Matrix ◽  
Delay Dependent

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.

Fault detection and isolation for discrete-time Markovian jump systems with generally bounded transition probabilities: A zonotope-based method

2021 ◽  
pp. 014233122110232
Author(s):  
Dunke Lu ◽  
Xinyu Zhang ◽  
Yunsheng Lan ◽  
Xiaohua Wang
Keyword(s):  
Fault Detection ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Fault Detection And Isolation ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Robust Observer ◽  
Robust Observers ◽  
Jump Systems

This paper addresses the fault detection and isolation for a class of discrete-time Markovian jump system with generally bounded transition probabilities. The proposed method is mainly based on a bank of [Formula: see text] robust observers, which can detect the actuator fault occurrence and, even more, can locate those subjected to the fault. Furthermore, the performance and the robustness of the designed [Formula: see text] robust observer are disseminated respect to disturbances and measurement noises. In particular, we propose the zonotop-based dynamic threshold to predict the ranges of the residual, which shows less conservatism in comparison to traditional methods. Finally, pertinent simulations are performed to corroborate the potential and superiority of the proposed method. In general, the proposed method offers effective fault detection and isolation scheme for Markovian jump systems, which can detect the fault timely and accurately with lowering the rate of fault missing report to a great extent, thus having practical value.

scholarly journals Robust ReliableH∞Control for Nonlinear Stochastic Markovian Jump Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Guici Chen ◽  
Yi Shen
Keyword(s):  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Stochastic Disturbance ◽  
Markovian Jump System ◽  
Actuator Failures ◽  
Jump Systems

The robust reliableH∞control problem for a class of nonlinear stochastic Markovian jump systems (NSMJSs) is investigated. The system under consideration includes Itô-type stochastic disturbance, Markovian jumps, as well as sector-bounded nonlinearities and norm-bounded stochastic nonlinearities. Our aim is to design a controller such that, for possible actuator failures, the closed-loop stochastic Markovian jump system is exponential mean-square stable with convergence rateαand disturbance attenuationγ. Based on the Lyapunov stability theory and Itô differential rule, together with LMIs techniques, a sufficient condition for stochastic systems is first established in Lemma 3. Then, using the lemma, the sufficient conditions of the solvability of the robust reliableH∞controller for linear SMJSs and NSMJSs are given. Finally, a numerical example is exploited to show the usefulness of the derived results.

H∞ model reduction for discrete singular Markovian jump systems

2009 ◽  
Vol 223 (7) ◽  
pp. 1017-1025 ◽  
Author(s):  
Z Wu ◽  
H Su ◽  
J Chu
Keyword(s):  
Model Reduction ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Bounded Real Lemma ◽  
Singular Markovian Jump Systems ◽  
Discrete Singular Systems ◽  
Jump Systems

The problem of H∞ model reduction is investigated for discrete singular systems with Markovian jump. A stochastic admissibility condition and bounded real lemma (BRL) are established for the discrete singular Markovian jump system in terms of the linear matrix inequality (LMI) approach. Under partial knowledge of the transition probabilities, the strict LMI-based sufficient condition is obtained for the existence of desired reduced-order model. The numerical example is proposed to show the validity of the developed result.

scholarly journals Filtering-Based Fault Detection for Stochastic Markovian Jump System with Distributed Time-Varying Delays and Mixed Modes

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Yucai Ding ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Jianwei Xia
Keyword(s):  
Fault Detection ◽  
Detection System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Stochastic Disturbance ◽  
Markovian Jump System ◽  
Stochastically Stable ◽  
Disturbance Attenuation Level

The problem of fault detection for stochastic Markovian jump system is considered. The system under consideration involves discrete and distributed time-varying delays, Itô-type stochastic disturbance, and different system and delay modes. The aim of this paper is to design a fault detection filter such that the fault detection system is stochastically stable and satisfies a prescribedH∞disturbance attenuation level. By using a novel Lyapunov functional, a mix-mode-dependent sufficient condition is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

scholarly journals H∞Control of Singular Markovian Jump Systems with Bounded Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongsheng Lin ◽  
Ying Li ◽  
Guoliang Wang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

This paper discussesH∞control problems of continuous-time and discrete-time singular Markovian jump systems (SMJSs) with bounded transition probabilities. Improved sufficient conditions for continuous-time SMJSs to be regular, impulse free, and stochastically stable withγ-disturbance attenuation are established via less conservative inequality to estimate the transition jump rates, so are the discrete-time SMJSs. With the obtained conditions, the design of a state feedback controller which ensures the resulting closed-loop system to be stochastically admissible and withH∞performance is given in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and the benefits of the proposed approaches.

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