scholarly journals RobustH∞Filtering for Discrete-Time Markov Jump Linear System with Missing Measurements

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yingjun Niu ◽  
Wei Dong ◽  
Yindong Ji
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Missing Measurements ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Error System ◽  
Markov Jump Linear System

The problem of robustH∞filtering is investigated for discrete-time Markov jump linear system (DMJLS) with uncertain parameters and missing measurements. The missing measurements process is modelled as a Bernoulli distributed sequence. A robustH∞filter is designed and sufficient conditions are established in terms of linear matrix inequalities via a mode-dependent Lyapunov function approach, such that, for all admissible uncertain parameters and missing measurements, the resulting filtering error system is robustly stochastically stable and a guaranteedH∞performance constraint is achieved. Furthermore, the optimalH∞performance index is subsequently obtained by solving a convex optimisation problem and the missing measurements effects on theH∞performance are evaluated. A numerical example is given to illustrate the feasibility and effectiveness of the proposed filter.

scholarly journals Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Ding Zhai ◽  
Liwei An ◽  
Jinghao Li ◽  
Qingling Zhang
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Feedback Controller ◽  
Sufficient Condition ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Markov Jump Linear System

This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

Robust H∞ Filtering for Stochastic Networked Control System with Nonlinearities and Missing Measurements

2012 ◽  
Vol 503-504 ◽  
pp. 1458-1462
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Yu Ping Zhang ◽  
Yong Zeng
Keyword(s):  
Control System ◽  
Sufficient Conditions ◽  
Networked Control System ◽  
Networked Control ◽  
Linear Matrix ◽  
Missing Measurements ◽  
Exponentially Stable ◽  
Inequality Technique ◽  
Error System ◽  
Linear Matrix Inequality Technique

This paper investigate the problem of Robust H∞ filtering for stochastic networked control system with nonlinearities and missing measurements. In this paper, missing measurements and nonlinearities are considered. The sufficient conditions for the existence of the filter are given, thus, guaranteeing the filter error system exponentially stable in the mean-square sense and the performance satisfies a prescribed level by employing the new Lyapunov-Krasovskii functional and linear matrix inequality technique, some new sufficient conditions are obtained.

Finite Time Passive Reliable Filtering for Fuzzy Systems With Missing Measurements

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
S. Vimal Kumar ◽  
R. Sakthivel ◽  
M. Sathishkumar ◽  
S. Marshal Anthoni
Keyword(s):  
Finite Time ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Missing Measurements ◽  
Randomly Occurring Uncertainties ◽  
Error System ◽  
Takagi Sugeno ◽  
Reliable Filtering

This paper investigates the problem of robust finite time extended passive reliable filtering for Takagi–Sugeno (T–S) fuzzy systems with randomly occurring uncertainties, missing measurements, and time-varying delays. Moreover, two stochastic variables satisfying the Bernoulli random distribution are introduced to characterize the phenomenon of the randomly occurring uncertainties and missing measurements. By skillfully choosing a proper Lyapunov–Krasovskii functional (LKF), a new set of sufficient conditions in terms of linear matrix inequalities (LMI) is derived to ensure that the filtering error system is robustly stochastically finite time bounded (SFTB) with a desired extended passive performance index. Based on the obtained sufficient conditions, an explicit expression for the desired filter can be computed. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design technique.

α− dissipative filtering for Singular Markov jump system with time delays

2022 ◽  
pp. 014233122110694
Author(s):  
Juan Zhou ◽  
HuiLing Lai ◽  
Bo Men
Keyword(s):  
Time Delays ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump System ◽  
Error System ◽  
Jump Systems ◽  
Dissipative Filtering ◽  
Partitioning Technique

This paper considers the [Formula: see text] dissipative filtering problem for a class of Singular Markov jump systems (SMJSs) with distributed time delays and discrete time delays. First, using Lyapunov’s stability theory and combining delay partitioning technique, integral partitioning technique, and free weight matrix method, the sufficient conditions for stochastic admissibility and [Formula: see text] dissipation of system are studied. Then, a filtering design method based on linear matrix inequalities (LMIs) is given to make the filtering error system stochastically admissible and [Formula: see text] dissipative. Finally, numerical simulations verify the effectiveness of the resulting method.

scholarly journals Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Fei Chen ◽  
Fei Liu ◽  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Space Representation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Finite Time Stabilization

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

Robust Stability and H∞ Control of Discrete-Time Jump Linear Systems With Time-Delay: An LMI Approach*

2003 ◽  
Vol 125 (2) ◽  
pp. 271-277 ◽  
Author(s):  
E. K. Boukas and ◽  
Z. K. Liu
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump System ◽  
System With Time Delay

This paper considers the class of discrete-time jump linear systems with time-delay and polytopic uncertain parameters. The problems of delay-independent robust stability, stabilization and H∞ control are cast into the framework of linear matrix inequality (LMI) and thus solved by LMI Toolbox of Matlab. By extending the system state, the system with time-delay is converted into a higher dimension Markov jump system without time-delay, and thus can be handled as a standard jump linear system with uncertain parameters. Numerical examples are provided to show the usefulness of the theoretical results.

scholarly journals H∞Filtering for a Class of Piecewise Homogeneous Markovian Jump Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yucai Ding ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Yong Zeng
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Attenuation Level ◽  
Stochastically Stable ◽  
Error System ◽  
Disturbance Attenuation Level ◽  
Filtering Problem

H∞filtering problem for a class of piecewise homogeneous Markovian jump nonlinear systems is investigated. The aim of this paper is to design a mode-dependent filter such that the filtering error system is stochastically stable and satisfies a prescribedH∞disturbance attenuation level. By using a new mode-dependent Lyapunov-Krasovskii functional, mixed mode-dependent sufficient conditions on stochastic stability are formulated in terms of linear matrix inequalities (LMIs). Based on this, the mode-dependent filter is obtained. A numerical example is given to illustrate the effectiveness of the proposed main results.

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