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Local Stabilization of Polynomial Fuzzy Model with Time Delay: SOS Approach
Hamdi Gassara,Ahmed El Hajjaji,Fatma Siala,Mohamed Chaabane 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.1
In this paper, a design method of control for Polynomial Fuzzy Models (PFM) with time delay is developed. By using a Polynomial Lyapunov Krasovskii Functional (PLKF) with double integral and by imposingbounds on the derivatives of each state, less conservative sufficient conditions are established to ensure the local stabilityof the closed loop system. Furthermore, a Domain Of Attraction (DOA) in which the initial states are ensuredto converge asymptotically to the origin is estimated. The resulting conditions are formulated in terms of Sum-Of-Squares (SOS) which can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. Some examples are provided to show the effectiveness and the merit of the design procedure.
Hamdi Gassara,Ahmed El Hajjaji,Mohamed Krid,Mohamed Chaabane 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.4
This paper investigates the problems of delay-dependent stability analysis and memory control design of polynomial fuzzy systems with time delay. Using polynomial Lyapunov-Krasovskii functional and slack polynomial matrix variables, delay dependent sufficient stability and stabilizability conditions are derived in terms of sum of squares (SOS) which can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. The main advantage of the proposed design is the reduction of conservatism for three great reasons. The first one is that polynomial matrices are not only dependent on the system state vector but also on the state vector with time delay. The second one is that the design conditions are formulated in delay dependent SOS. It is well known that the delay-dependent conditions are less conservative than those independent of time delay. The third one is that only correlated terms are used in the design of SOS. The simulation and comparison are given to illustrate the lesser conservativeness of the proposed result.
Dhouha Kharrat,Hamdi Gassara,Ahmed El Hajjaji,Mohamed Chaabane 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.3
This paper concerns the problem of state, fault estimation (FE) and Fault Tolerant Control (FTC) of Takagi-Sugeno (T-S) descriptor systems affected by sensor, actuator and external disturbances simultaneously. An Adaptive Fuzzy Observer is firstly proposed to achieve a simultaneous estimation of descriptor system states, actuator and sensor faults by using the H∞ optimization technique. A FTC is secondly proposed to stabilize the faulty descriptor system. Based on Lyapunov method, stability analysis and design conditions of the resulting closed-loop system are formulated in a set of Linear Matrices Inequalities (LMIs). The adaptive fuzzy observer and the FTC are independently designed, in order to avoid the coupling problem. Accordingly, the observer and controller gains are computed separately by solving a set of LMIs and then used to estimate the unmeasured states, sensor and actuator faults at the same time. Finally, a truck-trailer system application is given to illustrate the validity of the proposed approach.
Polynomial Dynamic Output-feedback Controllers for Positive Polynomial Fuzzy Systems with Time Delay
Imen Iben Ammar,Hamdi Gassara,Mohamed Chaabane,Ahmed El Hajjaji 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.8
This paper investigates the stability and stabilization problems of positive polynomial fuzzy uncertain interval models with time delay. Using the polynomial output feedback fuzzy control strategy, the design problem is firstly studied by considering the unmeasured states and measurable premise variables. Then, the control design problem is extended for both the unmeasurable states and unmeasurable premise variables. To study the considered analysis and design problems, a line-integral polynomial fuzzy Lyapunov function with polynomial terms depending of the estimated states is proposed. For each case, the proposed design conditions of the polynomial dynamic output feedback fuzzy controllers guarantying both the stability and the positivity of the resulting closed loop systems, are solved using the Sum of Squares (SOS) approach with tacking into account the positivity of the error signals. Finally, simulation examples are given to show the effectiveness of the proposed approaches.