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.

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 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.

scholarly journals Stochastic Stability for Time-Delay Markovian Jump Systems with Sector-Bounded Nonlinearities and More General Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Dan Ye ◽  
Quan-Yong Fan ◽  
Xin-Gang Zhao ◽  
Guang-Hong Yang
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Transition Probability Matrix ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Delay Dependent ◽  
Jump Systems

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

scholarly journals On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-23
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi
Keyword(s):  
Exponential Stability ◽  
Lyapunov Stability Theory ◽  
Markovian Jump Systems ◽  
Time Varying ◽  
Transition Rates ◽  
Stability Criteria ◽  
Markovian Jump ◽  
Rate Dependent ◽  
Partially Known Transition Rates ◽  
Jump Systems

The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Finite-Time Stabilization for Discrete-Time Delayed Markovian Jump Systems with Partially Delayed Actuator Saturation

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Guoliang Wang ◽  
Bo Feng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Controller Design ◽  
Actuator Saturation ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Time Control ◽  
Jump Systems

The finite-time control problem of discrete-time delayed Markovian jump systems with partially delayed actuator saturation is considered by a mode-dependent parameter approach. Different from the traditionally saturated actuators, a kind of saturated actuator being partially delay-dependent is firstly proposed, where both nondelay and delay states are included and occur asynchronously. Moreover, the probability distributions of such two terms are described by the Bernoulli variable and are taken into account in the controller design. Sufficient conditions for the existence of the desired controller are presented with LMIs. Finally, a numerical example is provided to show the effectiveness and superiority of the obtained results.

scholarly journals Resilient H-infinity filtering for networked nonlinear Markovian jump systems with randomly occurring distributed delay and sensor saturation

2021 ◽  
Vol 26 (2) ◽  
pp. 187-206
Author(s):  
Venkatesan Nithya ◽  
Rathinasamy Sakthivel ◽  
Yong Ren
Keyword(s):  
Sufficient Conditions ◽  
Distributed Delay ◽  
Random Variable ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Missing Measurements ◽  
Sensor Saturation ◽  
Jump Systems ◽  
Nonlinear Markovian Jump Systems

The H∞ filtering problem for a class of networked nonlinear Markovian jump systems subject to randomly occurring distributed delays, nonlinearities, quantization effects, missing measurements and sensor saturation is investigated in this paper. The measurement missing phenomenon is characterized via a random variable obeying the Bernoulli stochastic distribution. Moreover, due to bandwidth limitations, the measurement output is quantized using a logarithmic quantizer and then transmitted to the filter. Further, the output measurements are affected by sensor saturation since the communication links between the system and the filter are unreliable and is described by sector nonlinearities. The objective of this work is to design a quantized resilient filter that guarantees not only the stochastic stability of the augmented filtering error system but also a prespecified level of H∞ performance. Sufficient conditions for the existence of desired filter are established with the aid of proper Lyapunov–Krasovskii functional and linear matrix inequality approach together with stochastic analysis theory. Finally, a numerical example is presented to validate the developed theoretical results.

Finite-Time Observer Design for a Class of Markovian Jump Systems

2012 ◽  
Vol 482-484 ◽  
pp. 949-953
Author(s):  
Cheng Yong Xiao ◽  
Wei Ming Xiang
Keyword(s):  
Finite Time ◽  
Manufacturing Systems ◽  
Estimation Error ◽  
Observer Design ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Design Algorithm ◽  
Short Time ◽  
Jump Systems

Markovian jump systems are often used to model occurrence of failures and repairs in manufacturing systems. This note concerns the state estimation problem for a class of Markovian jump systems, where the Markovian jump only occurs in some short time intervals. For this class of Markovian jump systems, the boundness of estimation error deserves our investigation. By introducing the concepts of finite-time stochastic stability, an observer ensuring the estimation error bounded in a prescribed boundary is constructed and the result is extended to γ-disturbance attenuation case. A design algorithm is proposed when some parameter optimization is involved. Numerical design examples are given to illustrate the effectiveness of our results.

scholarly journals H∞Filtering for Networked Markovian Jump Systems with Multiple Stochastic Communication Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Hui Dong ◽  
Juntong Chen
Keyword(s):  
Filter Design ◽  
Design Method ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Communication Delays ◽  
Markovian Jump ◽  
Attenuation Level ◽  
Measurement Signal ◽  
Disturbance Attenuation Level ◽  
Jump Systems

This paper is concerned with theH∞filtering for a class of networked Markovian jump systems with multiple communication delays. Due to the existence of communication constraints, the measurement signal cannot arrive at the filter completely on time, and the stochastic communication delays are considered in the filter design. Firstly, a set of stochastic variables is introduced to model the occurrence probabilities of the delays. Then based on the stochastic system approach, a sufficient condition is obtained such that the filtering error system is stable in the mean-square sense and with a prescribedH∞disturbance attenuation level. The optimal filter gain parameters can be determined by solving a convex optimization problem. Finally, a simulation example is given to show the effectiveness of the proposed filter design method.

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