Robust and Non-Fragile H∞ Observer-Based Filter Design for Parameter Uncertain System Using PLMI Approach

2013 ◽  
Vol 373-375 ◽  
pp. 685-688
Author(s):  
Seung Hyeop Yang ◽  
Seung Hyun Paik ◽  
Hong Bae Park
Keyword(s):  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Uncertain System ◽  
Relaxation Technique ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Polytopic Uncertainties

This paper describes the synthesis of a robust and non-fragile H∞ observer-based filter design for a class of parameter uncertain system with polytopic uncertainties, disturbances, and gain variations. We present the sufficient condition for filter existence and the method for designing a robust and non-fragile H∞ filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use the relaxation technique to find finite solutions for a robust and non-fragile H∞ filter. We show that the proposed filter can minimize the estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

scholarly journals Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Seung Hyeop Yang ◽  
Hong Bae Park
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

Design of Robust and Non-Fragile Kalman Filter with Polytopic Uncertainties: PLMI Approach

2013 ◽  
Vol 284-287 ◽  
pp. 2356-2360
Author(s):  
Seung Hyeop Yang ◽  
Joon Ki Kim ◽  
Hong Bae Park
Keyword(s):  
Kalman Filter ◽  
Filter Design ◽  
Design Method ◽  
Linear Matrix ◽  
Compact Set ◽  
Sufficient Condition ◽  
Parameter Uncertainties ◽  
Uncertain Linear System ◽  
Finite Solution ◽  
Polytopic Uncertainties

In this paper, we describe the synthesis of robust and non-fragile Kalman filter design for a class of uncertain linear system with polytopic uncertainties and filter gain variations. The sufficient condition of filter existence, the design method of robust non-fragile filter, and the measure of non-fragility in filter are presented via LMIs(Linear Matrix Inequality) technique. And the obtained sufficient condition can be represented as PLMIs(Parameterized Linear Matrix Inequalities) that is, coefficients of LMIs are functions of a parameter confined to a compact set. Since PLMIs generate infinite LMIs, we use relaxation technique, find a finite solution for robust non-fragile filter, and show that the resulting filter guarantees the asymptotic stability with parameter uncertainties and filter fragility. Finally, a numerical example is shown to validate the proposed design method.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Robust Stabilization of Stochastic Markovian Jump Systems with Distributed Delays

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guilei Chen ◽  
Zhenwei Zhang ◽  
Chao Li ◽  
Dianju Qiao ◽  
Bo Sun
Keyword(s):  
Linear Matrix Inequalities ◽  
Robust Stabilization ◽  
Distributed Delays ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Delay Dependent ◽  
Jump Systems

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory.

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

2011 ◽  
Vol 317-319 ◽  
pp. 2204-2207
Author(s):  
Dong Mei Yang ◽  
Qing Sun
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Decentralized Control ◽  
Large Scale ◽  
Controller Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Large Scale Systems ◽  
System With Time Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

The Optimal Regulations of the Interconnection-Degrees of Large Scale Systems under Instable Case

2012 ◽  
Vol 235 ◽  
pp. 107-110
Author(s):  
Ying Ge Wo
Keyword(s):  
Cost Function ◽  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Large System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Large Scale Systems ◽  
The Cost

This paper discusses the stabilization problem of a large-scale system via cutting off the connections or decreasing the degree of interconnections among its subsystems subject to a cost function. Under the assumption that the large system is unstable but its sub-systems are all stable, a sufficient condition about the degree of interconnection is presented via cutting off the connections or decreasing the degree of interconnections among its subsystems such that the new large system is stable. This condition can be expressed by linear matrix inequalities (LMIs). Based on this analysis, an optimal regulation for such controls is obtained ensures the minimization of the cost function. An illustrating example is also given to show the effectiveness of the proposed 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.

Generalized dynamic observer design for quasi-LPV systems

2018 ◽  
Vol 66 (3) ◽  
pp. 225-233 ◽  
Author(s):  
A.-J. Pérez-Estrada ◽  
G.-L. Osorio-Gordillo ◽  
M. Darouach ◽  
V.-H. Olivares-Peregrino
Keyword(s):  
Linear Matrix Inequalities ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Algebraic Constraints ◽  
Dynamic Observer

Abstract This paper presents a new generalized dynamic observer (GDO) for quasi-linear parameter varying (LPV) systems. It generalises the structures of the proportional observer (PO) and proportional integral observer (PIO). The design of the GDO is derived from the solution of linear matrix inequalities (LMIs) and the solution of the algebraic constraints obtained from the estimation error analysis. The efficiency of the proposed approach is illustrated by a numerical example.

scholarly journals On the stability of 2D general Roesser Lyapunov systems

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 85-97
Author(s):  
Mohammed Amine Ghezzar ◽  
Djillali Bouagada ◽  
Kamel Benyettou ◽  
Mohammed Chadli ◽  
Paul Van Dooren
Keyword(s):  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
The Stability

This paper addresses the problem of stability for general two-dimensional (2D) discrete-time and continuous-discrete time Lyapunov systems, where the linear matrix inequalities (LMI's) approach is applied to derive a new sufficient condition for the asymptotic stability.

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