scholarly journals H∞ Filtering for Discrete-Time Nonlinear Singular Systems with Quantization

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yifu Feng ◽  
Zhi-Min Li ◽  
Xiao-Heng Chang
Keyword(s):  
Discrete Time ◽  
Filter Design ◽  
Design Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Nonlinear Singular Systems ◽  
Attenuation Level ◽  
Measurement Output

This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method.

Generalized H2 Filtering for Discrete-Time Switched Systems with Multiple Time-Varying Delays

2012 ◽  
Vol 562-564 ◽  
pp. 1646-1649 ◽  
Author(s):  
Rong You Zhang ◽  
Ni Zhang
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying

The generalized H2 filtering problem is investigated for linear discrete-time switched systems with multiple time-varying delays. By constructing the piecewise Lyapunov-Krasovskii functionals, employing Jensen inequality and slack variables, the delay-dependent sufficient conditions are derived for the filter-error system to be stable with a H2 performance. Based on the established results, the filter design method is presented in terms of the linear matrix inequalities (LMI). The design procedure is brief and easy to compute. The optimal filter can be solved with LMI toolbox of MATLAB directly. Finally, the simulation results illustrate the effectiveness and feasibility of the proposed method.

scholarly journals RobustH∞Filtering for Networked Control Systems with Random Sensor Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shenping Xiao ◽  
Liyan Wang ◽  
Hongbing Zeng ◽  
Lingshuang Kong ◽  
Bin Qin
Keyword(s):  
Networked Control Systems ◽  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Attenuation Level ◽  
Exponentially Stable ◽  
Disturbance Attenuation Level ◽  
Filter Design Method

The robustH∞filtering problem for a class of network-based systems with random sensor delay is investigated. The sensor delay is supposed to be a stochastic variable satisfying Bernoulli binary distribution. Using the Lyapunov function and Wirtinger’s inequality approach, the sufficient conditions are derived to ensure that the filtering error systems are exponentially stable with a prescribedH∞disturbance attenuation level and the filter design method is proposed in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by a numerical example.

scholarly journals RobustH∞Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yamin Wang ◽  
Fuad E. Alsaadi ◽  
Stanislao Lauria ◽  
Yurong Liu
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Attenuation Level ◽  
Discrete Time Delay ◽  
And Control

In this paper, we consider the robustH∞control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribedH∞disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained.

scholarly journals Robust Quantized GeneralizedH2Filtering for Uncertain Discrete-Time Fuzzy Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Jidong Wang ◽  
Xiaoping Si ◽  
Kezhen Han
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Noise Attenuation ◽  
Matrix Inequalities ◽  
Slack Variables ◽  
Fuzzy Lyapunov Function ◽  
Attenuation Level

This paper deals with the problem of robust generalizedH2filter design for uncertain discrete-time fuzzy systems with output quantization. Firstly, the outputs of the system are quantized by a memoryless logarithmic quantizer before being transmitted to a filter. Then, attention is focused on the design of a generalizedH2filter to mitigate quantization effects, such that the filtering error systems ensure the robust stability with a prescribed generalizedH2noise attenuation level. Via applying Finsler lemma to introduce some slack variables and using the fuzzy Lyapunov function, sufficient conditions for the existence of a robust generalizedH2filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

scholarly journals Network-Based RobustH∞Filtering for the Uncertain Systems with Sensor Failures and Noise Disturbance

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Mingang Hua ◽  
Pei Cheng ◽  
Juntao Fei ◽  
Jianyong Zhang ◽  
Junfeng Chen
Keyword(s):  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Uncertain System ◽  
Linear Matrix ◽  
Linear Filter ◽  
Parameter Uncertainties ◽  
Globally Asymptotically Stable ◽  
Sensor Failures ◽  
Filter Design Method

The network-based robustH∞filtering for the uncertain system with sensor failures and the noise is considered in this paper. The uncertain system under consideration is also subject to parameter uncertainties and delay varying in an interval. Sufficient conditions are derived for a linear filter such that the filtering error systems are robust globally asymptotically stable while the disturbance rejection attenuation is constrained to a given level by means of theH∞performance index. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is then given for the desired filter parameters. Two numerical examples are exploited to show the usefulness and effectiveness of the proposed filter design method.

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.

scholarly journals Fault Detection of Networked Control Systems Based on Sliding Mode Observer

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jie Zhang ◽  
Ming Lyu ◽  
Hamid Reza Karimi ◽  
Yuming Bo
Keyword(s):  
Fault Detection ◽  
Control Systems ◽  
Discrete Time ◽  
Networked Control Systems ◽  
Sliding Mode ◽  
Design Method ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Linear Matrix ◽  
Bounded Disturbances

This paper is concerned with the network-based fault detection problem for a class of nonlinear discrete-time networked control systems with multiple communication delays and bounded disturbances. First, a sliding mode based nonlinear discrete observer is proposed. Then the sufficient conditions of sliding motion asymptotical stability are derived by means of the linear matrix inequality (LMI) approach on a designed surface. Then a discrete-time sliding-mode fault observer is designed that is capable of guaranteeing the discrete-time sliding-mode reaching condition of the specified sliding surface. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

scholarly journals Synchronization and Control of Linearly Coupled Singular Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fang Qingxiang ◽  
Peng Jigen ◽  
Cao Feilong
Keyword(s):  
Singular Systems ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Coupling Matrix ◽  
The Stability ◽  
And Control

The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI), indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

scholarly journals H∞Observers Design for a Class of Continuous Time Nonlinear Singular Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed Zerrougui ◽  
Latifa Boutat-Baddas ◽  
Mohamed Darouach
Keyword(s):  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Minimal Order ◽  
Estimation Errors ◽  
Worst Case ◽  
Reduced Order ◽  
Lipschitz Continuous ◽  
Nonlinear Singular Systems ◽  
Error Energy

This paper considers the problem ofH∞observers design for a class of Lipschitz continuous nonlinear singular systems. The method is based on the parameterization of the solution of the generalized Sylvester equations obtained from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The approach also unifies the full-order, the reduced-order, and the minimal-order observers design. The solutions are obtained through linear matrix inequalities (LMIs) formulation. A numerical example is given to illustrate our results.

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