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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]

Summary: This paper addresses the sliding mode control problem for a class of uncertain Takagi‐Sugeno fuzzy singular systems with state delay and subject to input nonlinearity. Our purpose is focused on designing an adaptive sliding mode controller for such a complex system. First, a new fuzzy integral‐type sliding function is designed. Then, an adaptive sliding mode control scheme is established such that the resulting closed‐loop system is insensitive to all admissible uncertainties and satisfies the reaching condition. Moreover, delay‐dependent sufficient conditions are derived such that the admissibility and the L2‐L∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays, external disturbances, and sector nonlinearity input. Finally, the validity and applicability of the proposed theory are illustrated by a numerical example. [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 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]