scholarly journals Robust Filtering of 2D Roesser Discrete Systems: A Polynomial Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chakir El-Kasri ◽  
Abdelaziz Hmamed ◽  
Teresa Alvarez ◽  
Fernando Tadeo
Keyword(s):  
Estimation Error ◽  
State Space Model ◽  
Discrete Systems ◽  
Noise Signal ◽  
Linear Matrix ◽  
Robust Filtering ◽  
Matrix Inequalities ◽  
Error System ◽  
2D Discrete Systems ◽  
Parameter Dependent

The problem of robust filtering is investigated for the class of uncertain two-dimensional (2D) discrete systems described by a Roesser state-space model. The main contribution is a systematic procedure for generating conditions for the existence of a 2D discrete filter such that, for all admissible uncertainties, the error system is asymptotically stable, and the norm of the transfer function from the noise signal to the estimation error is below a prespecified level. These conditions are expressed as parameter-dependent linear matrix inequalities. Using homogeneous polynomially parameter-dependent filters of arbitrary degree on the uncertain parameters, the proposed method extends previous results in the quadratic framework and the linearly parameter-dependent framework, thus reducing its conservatism. Performance of the proposed method, in comparison with that of existing methods, is illustrated by two examples.

Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

2020 ◽  
Vol 37 (4) ◽  
pp. 1114-1132
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Mohamed Oubaidi ◽  
Zakaria Chalh
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Error System ◽  
Parameter Dependent

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the proposed method.

Robust H∞ deconvolution filter for polytopic uncertain systems with distributed delay

2017 ◽  
Vol 40 (11) ◽  
pp. 3368-3376 ◽  
Author(s):  
Weifeng Xia ◽  
Shengyuan Xu
Keyword(s):  
Uncertain Systems ◽  
Distributed Delay ◽  
Functional Method ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Polytopic Uncertain Systems ◽  
Parameter Dependent ◽  
Filtering Problem

This paper is concerned with the robust H∞ deconvolution filtering problem for polytopic uncertain systems with distributed delay. The objective is to design a full-order deconvolution filter such that the filtering error system is not only asymptotically stable, but also satisfies a prescribed H∞ performance level for all uncertainties. Based on employing the parameter-dependent Lyapunov–Krasovskii functional method, a sufficient condition is proposed for solvability of this problem in terms of linear matrix inequalities. In order to reduce the conservatism, two approaches, namely, the integral partitioning approach, and the homogeneous polynomial parameter-dependent matrix approach, are applied. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed methods in this paper.

scholarly journals Design of unknown input fractional-order observers for fractional-order systems

2013 ◽  
Vol 23 (3) ◽  
pp. 491-500 ◽  
Author(s):  
Ibrahima N’Doye ◽  
Mohamed Darouach ◽  
Holger Voos ◽  
Michel Zasadzinski
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Order Error ◽  
Error System ◽  
Time Linear

Abstract This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

2011 ◽  
Vol 20 (04) ◽  
pp. 657-666
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Estimation Error ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
State Estimator ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

Multi-Model Adaptive Regulation for Aircraft Dynamics With Different Zero Structures

2014 ◽  
Author(s):  
Eric D. Peterson ◽  
Harry G. Kwatny
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Linear Matrix ◽  
Model Design ◽  
Multiple Model ◽  
Matrix Inequalities ◽  
Adaptive Regulation ◽  
Aircraft Dynamics ◽  
Adaptive Regulator ◽  
Parameter Dependent

An adaptive regulator is designed for parameter dependent families of systems subject to changes in the zero structure. Since continuous adaptive regulation is limited by relative degree and right half plane zeros, a multiple model adaptive regulator is implemented. The two multiple model design subproblems, covering and switching, are addressed with LQR state feedback and Lyapunov function switch logic respectively. These two subproblems are combined into a set of Linear Matrix Inequalities (LMI) and concurrently solved. The multiple model design method is applied to longitudinal aircraft dynamics.

scholarly journals Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Emerson R. P. da Silva ◽  
Edvaldo Assunção ◽  
Marcelo C. M. Teixeira ◽  
Luiz Francisco S. Buzachero
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Finsler’S Lemma ◽  
Time Linear

The motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

scholarly journals Delay-Dependent RobustH∞Filtering of the Takagi-Sugeno Fuzzy Stochastic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Ze Li ◽  
Xin-Hao Yang
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Mean Square Stability ◽  
Error System ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper is concerned with the problem of the robustH∞filtering for the Takagi-Sugeno (T-S) fuzzy stochastic systems with bounded parameter uncertainties. For a given T-S fuzzy stochastic system, this paper focuses on the stochastically mean-square stability of the filtering error system and theH∞performance level of the output error and the disturbance input. The design method for delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed methods is substantiated with an illustrative example.

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 Model reduction design for continuous systems with finite frequency specifications

2021 ◽  
Vol 11 (5) ◽  
pp. 3956
Author(s):  
Miloud Koumir ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Error System ◽  
Takagi Sugeno

<p>This paper is concerned with the problem of model reduction design for continuous systems in Takagi-Sugeno fuzzy model. Through the defined FF H∞ gain performance, sufficient conditions are derived to design model reduction and to assure the fuzzy error system to be asymptotically stable with a FF H∞ gain performance index. The explicit conditions of fuzzy model reduction are developed by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.</p>

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