Proceedings ArticleDOI
H∞ Model Reduction for Two-Dimensional Discrete Systems in Finite Frequency Ranges
Abderrahim El-Amrani,Ahmed El Hajjaji,Bensalem Boukili,Abdelaziz Hmamed +3 more
- pp 885-890
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TLDR
Using the well-known generalized lemma of Kalman Yakubovich Popov and the Finsler's lemma, sufficient conditions for the existence of the reduction of the H∞ model for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs).Abstract:
This paper examines the design problem H∞ of the reduced order model for two-dimensional (2D) discrete systems described by the Roesser model with a control input assumed to operate in a finite frequency (FF) domain. Given an asymptotically stable system; our goal is to find a stable reduced order system so that the error of the transfer functions between the original system and the reduced order is limited to a range FF. Using the well-known generalized lemma of Kalman Yakubovich Popov (gKYP) and the Finsler's lemma, sufficient conditions for the existence of the reduction of the H∞ model for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). An illustrative example is provided to show the utility and potential of the proposed results.read more
Citations
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Proceedings ArticleDOI
Finite Frequency Approach for H∞ model reduction of 2D continuous systems
TL;DR: Using the well known generalized Kalman Yakubovich Popov Lemma and the Finsler's Lemma, sufficient conditions for the existence of H∞ model reduction for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs).
Journal ArticleDOI
Improved filtering H∞ finite frequency of Takagi-Sugeno fuzzy systems
TL;DR: The simulation results are provided to show the effectiveness and the validity of the proposed FF H∞ T-S fuzzy filter method of FM LSS models strategy by a practical application.
Proceedings ArticleDOI
H ∞ Analysis For Descriptor Systems: A Strict LMI Approach
TL;DR: In this paper, the performance of the descriptor system with continuous-time was studied and the sufficient condition was given in form of strict LMI for the problem that such descriptor systems are admissible with disturbance attenuation level.
Proceedings ArticleDOI
H ∞ Control in Middle Frequency for 2D continuous systems
TL;DR: In this article, a new H ∞ state feedback control with new conditions in middle frequency domains is proposed, and the stability and robustness conditions are converted into linear matrix inequality forms which can be solved directly by convex optimization technique.
Proceedings ArticleDOI
On H ∞ Filtering for continuous-time Takagi-Sugeno Fuzzy Systems in Low frequency domain
TL;DR: A new design sufficient condition via linear matrix Inequality (LMIs) formulations is proposed, ensuring that the error system is stable and has a minimized $H_{\infty}$ performance when frequency ranges of noises are known beforehand.
References
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Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
TL;DR: This paper describes how to work with SeDuMi, an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints by exploiting sparsity.
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All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†
TL;DR: In this paper, a complete characterization of all rational functions that minimize the Hankel-norm is derived, and the solution to the latter problem is via results on balanced realizations, all-pass functions and the inertia of matrices, all in terms of the solutions to Lyapunov equations.
Book
Approximation of Large-Scale Dynamical Systems
TL;DR: This paper presents SVD-Krylov Methods and Case Studies, a monograph on model reduction using Krylov methods for linear dynamical systems, and some examples of such reduction schemes.
Journal ArticleDOI
A discrete state-space model for linear image processing
TL;DR: In this paper, the linear time-discrete state-space model is generalized from single-dimensional time to two-dimensional space, which includes extending certain basic known concepts from one to two dimensions, such as the general response formula, state transition matrix, Cayley-Hamilton theorem, observability, and controllability.
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