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The delay-dependent state, Fault Estimation (FE) and Fault Tolerant Control problems for polynomial fuzzy systems with time delay are investigated in this paper. Firstly, a polynomial adaptive fuzzy observer is used to estimate system states and actuator faults. A polynomial Lyapunov–Krasovskii functional including double integral term is introduced in order to obtain delay-dependent sufficient conditions in terms of Sum Of Squares (SOS) which can be solved via SOSTOOLS and a Semi-Definite Program solver. Then, by exploiting the FE information, a polynomial fuzzy fault tolerant controller is designed to guarantee the stability of the system and to compensate the impact of actuator faults. Finally, several examples are given to illustrate the use of the present delay-dependent result. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper investigates both fault estimation and fault-tolerant control problems for polynomial systems with state delay in presence of faults. Before studying the control problem, a polynomial observer is proposed to jointly estimate state and fault vectors. Based on the obtained informations, a polynomial controller is designed to compensate fault effects and to stabilize the closed-loop systems even in presence of state delay. The existence of both polynomial observer and controller is proved via satisfying sufficient conditions based on a sum of square (SOS) approach. Polynomial observer and controller gains are computed using SOSTOOLS. Finally, a numerical example is given to demonstrate that the SOS approach provides a significant improvement in reaction to fault occurrence for time delay systems. Furthermore, a tunnel diode circuit and a mass–spring–damper system are used to illustrate the applicability of the design method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of state/fault estimation and active fault-tolerant control (AFTC) design for time-delay descriptor fuzzy systems subject to external disturbances and actuator faults. Using Takagi-Sugeno fuzzy models, an adaptive fuzzy observer is proposed to achieve system state and actuator fault estimation simultaneously. According to Lyapunov functional method, design and analysis conditions of the resulting closed-loop delayed descriptor system are formulated in terms of linear matrices inequalities (LMIs). Observer and controller gains are computed by solving a set of LMIs in only one step and then used to both estimate the unmeasured states and actuator faults in AFTC context. Numerical examples are provided to show the merit and the conservativeness of the proposed approach in comparison with the existing methods by considering various types of actuator faults. [ABSTRACT FROM AUTHOR]

This paper presents a new Line-integral polynomial Lyapunov functional approach for observer-based control for a class of polynomial fuzzy systems with time delay and unmeasured state variables. To guarantee the global asymptotic stability and estimation error convergence, a design method is proposed. In this work we consider a Line-integral polynomial Lyapunov function in which the Lyapunov matrices are polynomial matrices depending not only of the estimated states but also of the estimated delayed states and we use the dual system to reduce the computational efforts. The design conditions are established in terms of Sum Of Squares (SOS) which can be numerically and symbolically solved via the recent developed SOSTOOLS and a Semi-Definite Program solver. Finally, numerical examples are proposed to show the validity and applicability of the proposed results. [ABSTRACT FROM AUTHOR]

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 imposing bounds on the derivatives of each state, less conservative sufficient conditions are established to ensure the local stability of the closed loop system. Furthermore, a Domain Of Attraction (DOA) in which the initial states are ensured to 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. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability and stabilization of polynomial fuzzy systems with time delay. This study is based on a polynomial Lyapunov-Krasovskii functional, and delay-dependent results are described in terms of bilinear sum of squares (SOS) conditions. Two techniques are presented, in this paper, to solve the problem of non-convexity of SOS stability and stabilization conditions for polynomial fuzzy systems with time delay. The first technique presents the SOS stability conditions for a specific class of polynomial fuzzy systems with time delay. Delay-dependent conditions are derived throughout a predefined set of indices. This technique improves delay-independent results existing in the literature. The second method transforms the design problem on an optimization problem subject to SOS constraints. The proposed SOS approach is more innovative and effective than the existing linear matrix inequality in terms of conservatism reduction. The new convex conditions for polynomial fuzzy systems with time delay are shown in terms of SOS which can be solved via SOSTOOLS software. Numerical examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article is concerned with the design of polynomial fuzzy controller for a class of polynomial fuzzy model subject to both state delay and actuator saturation. Based on polytopic model of the input saturation, two design methods are proposed. In the first method, a specific Lyapunov Krasovskii function is proposed to transform the nonconvex sum of squares (SOS) conditions into convex SOS ones. The second method overcomes the restriction of the first method by bounding the state derivative. The obtained results are formulated in terms of SOS matrices which can be symbolically and numerically solved via the SOSTOOLS and the SeDuMi. Moreover, an attractive region of initial states that ensures asymptotic stability of polynomial fuzzy model is determined. Two numerical examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem of time delay fuzzy descriptor system under actuator saturation. A polytopic approach is used to describe the saturation behavior. By using an augmented Lyapunov-Krasovskii functional and adopting the delay partitioning technique, less conservative sufficient conditions are established to ensure the closed-loop system to be locally robust admissible. Moreover, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is determined. In this paper, all the conditions are transformed into minimization problem involving LMI conditions by adopting the idea of the cone complementarity algorithm. This minimization problem can be solved efficiently by using the LMI optimization techniques. A numerical example illustrates the effectiveness of the design. [ABSTRACT FROM AUTHOR]