2019 |
Gasmi, Noussaiba; Thabet, Assem; Aoun, Mohamed New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results Article de journal Dans: International Journal of Automation and Computing, vol. 16, no. 5, p. 644 – 654, 2019, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Arduino, Asymptotic stability, Degrees of freedom (mechanics), Digital control systems, Discrete – time systems, Discrete time control systems, Linear matrix inequalities, Lipschitz systems, Performance analysis, Real time control, Reduced order observers @article{Gasmi2019644b,The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems. The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities (LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H∞ performance analysis is considered in order to deal with H∞ asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device. © 2018, Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature. |
Gasmi, Noussaiba; Thabet, Assem; Aoun, Mohamed New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results Article de journal Dans: International Journal of Automation and Computing, vol. 16, no. 5, p. 644 – 654, 2019, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Arduino, Asymptotic stability, Degrees of freedom (mechanics), Digital control systems, Discrete – time systems, Discrete time control systems, Linear matrix inequalities, Lipschitz systems, Performance analysis, Real time control, Reduced order observers @article{Gasmi2019644,The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems. The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities (LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H∞ performance analysis is considered in order to deal with H∞ asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device. © 2018, Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature. |
2018 |
Gasmi, Noussaiba; Boutayeb, Mohamed; Thabet, Assem; Aoun, Mohamed Enhanced LMI conditions for observer-based H∞ stabilization of Lipschitz discrete-time systems Article de journal Dans: European Journal of Control, vol. 44, p. 80 – 89, 2018, (Cited by: 8). Résumé | Liens | BibTeX | Étiquettes: Control nonlinearities, Controller designs, Controllers, Decoding, Delayed state, Digital control systems, Discrete – time systems, Discrete time control systems, Linear matrix inequalities, Linear matrix inequality approach, Lipschitz systems, Noise analyse, Observer-based controller design, Observer-based controllers, Robustness (control systems), Sliding Window, Sliding window of measurement @article{Gasmi201880b,This paper deals with H∞ observer-based controller design for a class of discrete-time systems with Lipschitz nonlinearities. Usually, the observer-based control synthesis for the considered class of systems leads to the feasibility of a Bilinear Matrix Inequality (BMI). Since, solving a BMI constraint has been an NP-hard optimization problem, then linearizing this constraint to get a convex one is an interesting issue because Linear Matrix Inequalities (LMIs) are easily tractable by numerical softwares (LMI Toolboxes,.). Hence, the aim of this paper is to develop a new Linear Matrix Inequality (LMI) condition, ensuring the H∞ asymptotic convergence of the observer-based controller. Due to the introduction of a slack variable technique, the usual BMI problem is equivalently transformed to a more suitable one, which leads to less conservative and more general LMI condition compared to the existing methods in the literature. Conjointly to the slack variable technique, the Lipschitz property and the Young’s relation are used in a reformulated way to obtain additional decision variables in the LMI. In the aim to further relax the proposed LMI methodology, sliding windows of delayed states and measurements are included in the structures of the controller and the observer, respectively. The obtained LMI is more general and less conservative than the first one, which can be viewed as a particular solution. To show the effectiveness and superiority of the proposed methodology, some numerical examples and comparisons are provided. © 2018 European Control Association |
Gasmi, Noussaiba; Boutayeb, Mohamed; Thabet, Assem; Aoun, Mohamed Enhanced LMI conditions for observer-based H∞ stabilization of Lipschitz discrete-time systems Article de journal Dans: European Journal of Control, vol. 44, p. 80 – 89, 2018, (Cited by: 8). Résumé | Liens | BibTeX | Étiquettes: Control nonlinearities, Controller designs, Controllers, Decoding, Delayed state, Digital control systems, Discrete – time systems, Discrete time control systems, Linear matrix inequalities, Linear matrix inequality approach, Lipschitz systems, Noise analyse, Observer-based controller design, Observer-based controllers, Robustness (control systems), Sliding Window, Sliding window of measurement @article{Gasmi201880,This paper deals with H∞ observer-based controller design for a class of discrete-time systems with Lipschitz nonlinearities. Usually, the observer-based control synthesis for the considered class of systems leads to the feasibility of a Bilinear Matrix Inequality (BMI). Since, solving a BMI constraint has been an NP-hard optimization problem, then linearizing this constraint to get a convex one is an interesting issue because Linear Matrix Inequalities (LMIs) are easily tractable by numerical softwares (LMI Toolboxes,.). Hence, the aim of this paper is to develop a new Linear Matrix Inequality (LMI) condition, ensuring the H∞ asymptotic convergence of the observer-based controller. Due to the introduction of a slack variable technique, the usual BMI problem is equivalently transformed to a more suitable one, which leads to less conservative and more general LMI condition compared to the existing methods in the literature. Conjointly to the slack variable technique, the Lipschitz property and the Young’s relation are used in a reformulated way to obtain additional decision variables in the LMI. In the aim to further relax the proposed LMI methodology, sliding windows of delayed states and measurements are included in the structures of the controller and the observer, respectively. The obtained LMI is more general and less conservative than the first one, which can be viewed as a particular solution. To show the effectiveness and superiority of the proposed methodology, some numerical examples and comparisons are provided. © 2018 European Control Association |
Publications
2019 |
New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results Article de journal Dans: International Journal of Automation and Computing, vol. 16, no. 5, p. 644 – 654, 2019, (Cited by: 0). |
New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results Article de journal Dans: International Journal of Automation and Computing, vol. 16, no. 5, p. 644 – 654, 2019, (Cited by: 0). |
2018 |
Enhanced LMI conditions for observer-based H∞ stabilization of Lipschitz discrete-time systems Article de journal Dans: European Journal of Control, vol. 44, p. 80 – 89, 2018, (Cited by: 8). |
Enhanced LMI conditions for observer-based H∞ stabilization of Lipschitz discrete-time systems Article de journal Dans: European Journal of Control, vol. 44, p. 80 – 89, 2018, (Cited by: 8). |