scholarly journals H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cheng Gong ◽  
Yi Zeng
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Singular Systems ◽  
Fuzzy Model ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Delay Dependent ◽  
Jump Systems

This paper investigates theH∞filtering problem of discrete singular Markov jump systems (SMJSs) with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition onH∞-disturbance attenuation is presented, in which both stability and prescribedH∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependentH∞filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

scholarly journals Positiveness and Observer-Based Finite-Time Control for a Class of Markov Jump Systems with Some Complex Environment Parameters

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Chengcheng Ren ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
Complex Environment ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Time Control ◽  
Jump Systems ◽  
Environment Parameters

An observer-based finite-time L2-L∞ control law is devised for a class of positive Markov jump systems in a complex environment. The complex environment parameters include bounded uncertainties, unknown nonlinearities, and external disturbances. The objective is to devise an appropriate observer-based control law that makes the corresponding augment error dynamic Markov jump systems be positive and finite-time stabilizable and satisfy the given L2-L∞ disturbance attenuation index. A sufficient condition is initially established on the existence of the observer-based finite-time controller by using proper stochastic Lyapunov-Krasovskii functional. The design criteria are presented by means of linear matrix inequalities. Finally, the feasibility and validity of the main results can be illustrated through a numerical example.

Fuzzy model-based asynchronous H∞ filter design of discrete-time Markov jump systems

2017 ◽  
Vol 354 (18) ◽  
pp. 8444-8460 ◽  
Author(s):  
Meng Zhang ◽  
Peng Shi ◽  
Zhitao Liu ◽  
Hongye Su ◽  
Longhua Ma
Keyword(s):  
Discrete Time ◽  
Filter Design ◽  
Fuzzy Model ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Model Based ◽  
Jump Systems

scholarly journals Dissipativity-based asynchronous control for discrete-time singular Markov jump systems with multiplicative noises

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985161
Author(s):  
Xiao Lu ◽  
Jiaqiang Yan ◽  
Haixia Wang ◽  
Chunyang Sheng ◽  
Zhiguo Zhang ◽  
...  
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Output Measurement ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.

scholarly journals Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 187
Author(s):  
Khalid A. Alattas ◽  
Ardashir Mohammadzadeh ◽  
Saleh Mobayen ◽  
Hala M. Abo-Dief ◽  
Abdullah K. Alanazi ◽  
...  
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Polytopic Uncertainties ◽  
Jump Systems ◽  
Special Case ◽  
Stable Control

The Markov jump systems (MJSs) are a special case of parametric switching system. However, we know that time delay inevitably exists in many practical systems, and is known as the main source of efficiency reduction, and even instability. In this paper, the stochastic stable control design is discussed for time delay MJSs. In this regard, first, the problem of modeling of MJSs and their stability analysis using Lyapunov-Krasovsky functions is studied. Then, a state-feedback controller (SFC) is designed and its stability is proved on the basis of the Lyapunov theorem and linear matrix inequalities (LMIs), in the presence of polytopic uncertainties and time delays. Finally, by various simulations, the accuracy and efficiency of the proposed methods for robust stabilization of MJSs are demonstrated.

scholarly journals Dissipative Filter Design for Nonlinear Time-Varying-Delay Singular Systems against Deception Attacks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Guobao Liu ◽  
Shibin Shen ◽  
Xianglei Jia
Keyword(s):  
Filter Design ◽  
Singular Systems ◽  
Signal Transmission ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Measurement Output ◽  
Delay Dependent ◽  
Varying Delay

This paper applies a T-S fuzzy model to depict a class of nonlinear time-varying-delay singular systems and investigates the dissipative filtering problem for these systems under deception attacks. The measurement output is assumed to encounter random deception attacks during signal transmission, and a Bernoulli distribution is used to describe this random phenomena. In this case, the filtering error system modeled by a stochastic singular T-S fuzzy system is established and stochastic admissibility for this kind of system is defined firstly. Then, by combining some integral inequalities and using the Lyapunov–Krasovskii functional approach, sufficient delay-dependent conditions are presented based on linear matrix inequality techniques, where the system of filtering error can be stochastically admissible and strictly ℚ , S , ℝ -dissipative against randomly occurring deception attacks. Moreover, parameters of the desired filter can be obtained via the solutions of the established conditions. The validity of our work is illustrated through a mostly used example of the nonlinear system.

H∞ Filtering for Markov Jump Systems with Mixed Modes

2013 ◽  
Vol 706-708 ◽  
pp. 585-588
Author(s):  
Shu Lv ◽  
Shou Ming Zhong ◽  
Yu Cai Ding
Keyword(s):  
Stochastic Stability ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Attenuation Level ◽  
Stochastically Stable ◽  
Disturbance Attenuation Level ◽  
System Mode ◽  
Jump Systems

In this study, H_infinity filtering problem for a class of stochastic Markov jump systems is investigated. The system mode is assumed to be different from the delay mode. The aim of this paper is to design a mode-dependent filter such that the filtering error system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a mode-dependent Lyapunov functional, mixed mode-dependent sufficient condition on stochastic stability is formulated in terms of linear matrix inequalities. Based on the stochastic stability criterion, an H_infinity filter is developed.

scholarly journals RobustH∞Filtering for Uncertain Neutral Stochastic Systems with Markovian Jumping Parameters and Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Yajun Li ◽  
Zhaowen Huang
Keyword(s):  
Time Delay ◽  
Stochastic Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Stochastically Stable ◽  
Neutral Stochastic Systems ◽  
Error System ◽  
Delay Dependent

This paper deals with the robustH∞filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribedH∞performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.

Sign in / Sign up

Export Citation Format

Share Document