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30th Mediterranean Conference on Control and Automation (MED), Athens, GREECE, JUN 28-JUL 01, 2022; International audience; In this work, robustness and convergence properties of model reduction are investigated for discrete two-dimensional (2D) systems in the Fornasini-Marchesini (F-M) model with polytopic uncertainties. The goal is to design a reduced order model minimizing H-infinity performance in a known finite-frequency (FF) area of the noises able to reproduce the behavior of the uncertain 2D original system. Using Lyapunov function and generalized Kalman Yakubovich Popov (gKYP) lemma, sufficient conditions for the existence of the FF reduced order design approach are formulated as feasibility of a set of Linear Matrix Inequalities (LMIs). Numerical simulations are given to illustrate the validity and feasibility of the designed reduced-order model.

International audience; This article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.

International audience; This paper deals with the problem of robust H∞ model reduction for two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties, over finite frequency (FF) domain. The problem to be solved in the paper is to find a reduced-order model such that the approximation error system is asymptotically stable, which is able to approximate the original continuous systems system with comparatively small and minimised H∞ performance when frequency ranges of noises are known beforehand. Via the use of the generalised Kalman Yakubovich Popov (gKYP) lemma, homogeneous polynomially parameter-dependent matrices, Finsler's lemma and we introduce many slack matrices, 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). To highlight the effectiveness of the proposed H∞ model reduction design, two illustrative examples are given.

International audience

This study deals with (Q,S,R)-γ-dissipative output feedback control design for a class of switched systems with time-varying delay and unmeasurable states. The purpose is to design an observer-based controller and a switching rule to ensure both exponential stability and strict dissipativity of the resulting closed-loop switched systems. Using an augmented switched Lyapunov-Krasovskii functional with triple sum and the improved reciprocally convex combination approach, new sufficient conditions are developed in terms of linear matrix inequalities. Simulation examples are included to demonstrate the validity and effectiveness of the proposed design technique.

The aim of this article is to present the planetary gear tooth fault detection using stator current space vector analysis in steady-state working condition of induction machine-based systems. For this study a universal method is used. The proposed technique is mainly relied on the computation of a transfer function which defines the response of the stator current space vector to the perturbations induced by gear tooth fault of the planetary gear located within the drive train. The idea of electrical-mechanical analogy is employed to facilitate the computation of the mentioned transfer function. This approach is considered as an upstream phase for studying the feasibility of gear tooth fault diagnosis using non-invasive measurement. A fault index is recommended for the fault severity evaluation at different levels of the mechanical load. The performance of the proposed fault index is validated through experiments using a representative induction machine-based test rig which includes a three-phase 5.5kW wound rotor induction machine connected to a fixed ring single-stage planetary gearbox.

In this paper, the output feedback controller is designed for the 2D discrete (T-S) fuzzy systems expressed by Fornasini-Marchesini II Model. Our aim is to develop static output feedback controller (SOF) so that the addressed closed loop system globally asymptotically stable. By using the fuzzy-basis-dependent Lyapunov function only, sufficient conditions are given in form of linear matrix inequalities (LMIs) to guarantee the 2D closed loop system to be globally asymptotically stable. The main advantage is design a SOF controller is that no constraints are imposed on system matrices. Illustrative example is given to show the potential and usefulness of the proposed results.

27th Mediterranean Conference on Control and Automation, Akko, ISRAEL, JUL 01-04, 2019; International audience; This paper considers the problem of H-infinity model reduction problem with finite frequency (FF) ranges of the input vector for two-dimensional (2D) continuous systems. Given an asymptotically stable system, the main objective is to find a stable reduced-order model such that the error of the transfer functions between the original system and the reduced-order one is bounded over a FF range. Using the well known generalized Kalman Yakubovich Popov (gKYP) Lemma and the Finsler's Lemma, sufficient conditions for the existence of H-infinity model reduction for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is illustrated by a numerical example.

This paper considers the problem of H∞ model reduction problem with finite frequency (FF) ranges of the input vector for two-dimensional (2D) continuous systems. Given an asymptotically stable system, the main objective is to find a stable reduced-order model such that the error of the transfer functions between the original system and the reduced-order one is bounded over a FF range. Using the well known generalized Kalman Yakubovich Popov (gKYP) 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). Finally, the effectiveness of the proposed method is illustrated by a numerical example.

This study investigates the problem of robust observer design for a class of one-sided non-linear continuous-time systems with parameter uncertainties and $L_{2}$L2 bounded admissible external disturbance. The one-sided Lipschitz and quadratically inner-bounded conditions have been utilised to derive less conservative synthesis condition for the observer design. The corresponding design methodology is established, with the help some special derivations, bilinear matrix inequalities are successfully transformed into a set of linear matrix inequalities. Then, the robust controller and observer gains can be simultaneously found at one step. Finally, two numerical examples are given to illustrate the validity and the effectiveness of the proposed method.

International audience