Sugeno Fuzzy Descriptor Research Articles

Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors

This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system.

Admissibility analysis of Takagi–Sugeno fuzzy descriptor systems with time-varying delay via nonorthogonal free-matrix-based inequality

This paper studies the admissibility of Takagi–Sugeno (T-S) fuzzy descriptor systems with time-varying delay. To analyze the admissibility, various free-matrix-based inequalities (FMIs) are used in the existing works, since they directly produce bounds for integral terms without time-varying delay in denominator. However, the slack matrices in these inequalities are incomplete with some zero components, which may lead to incomplete coupling system information. In this case, conservatism is unavoidable. To remove the issue, a nonorthogonal FMI (NFMI) is proposed by constructing nonorthogonal polynomials with auxiliary scalars and auxiliary vectors, which includes some existing FMIs as its special cases. Based on the NFMI, a less conservative admissibility criterion is obtained for T-S fuzzy descriptor system. Two examples are illustrated to demonstrate the effectiveness of the obtained results.

Improvements on stability conditions and control design of Takagi–Sugeno fuzzy descriptor systems

Several methods to improve stabilization conditions of Takagi–Sugeno fuzzy descriptor systems (TSFDS) are presented. First, we prove that with a modified non–quadratic fuzzy Lyapunov function and a PDC controller, stabilization problems of TSFDS are reformulated as checking negativity of ”triple” fuzzy summations, and then relaxed methods of T–S fuzzy systems can be directly applied to descriptor systems. In the sequel, two relaxed methods are extended to TSFDS based on slack decision variables and Polya’s Theorem, respectively, but these conditions are only sufficient. Second, we design a non–quadratic fuzzy Lyapunov function which simultaneously consists of membership functions of derivative matrices and state matrices, and it generalizes previous related Lyapunov functions. Then with a non–PDC controller, not only sufficient but asymptotically necessary conditions for TSFDS are presented based on Polya’s theorem. All conditions are cast into LMIs, and simulation examples illustrate improvements and effectiveness of these methods.

Robust [formula omitted] observer-based sliding mode control for uncertain Takagi–Sugeno fuzzy descriptor systems with unmeasurable premise variables and time-varying delay

This work focuses on the observer-based sliding mode control (OBSMC) synthesis for non-linear T-S fuzzy descriptor time-varying delay systems, which subject to uncertainties and unmeasurable premise variables (UPVs). Due to the state variables are difficult to completely accessible, a sliding mode observer (SMO) is designed to estimate the unmeasurable variables, and the nonlinear systems are represented to an equivalent multiple model (MM) forms under the MM formulation with UPVs. Then two sliding surfaces are proposed for the observer system and error system respectively to ensure stabilization, which can effectively deal with the nonlinearity and uncertainties as well. By the utilization of the linear matrix inequality (LMI) technique, we present the stability criterions such that the sliding mode dynamics with H∞ performance are proved to be admissible. Moreover, the SMC is obtained so we can drive the system trajectories to the predefined sliding surface in a finite time. At last, three simulation examples are provided to certificate the availability of our approach.

Admissibility Analysis and Robust ${H_\infty }$ Control for T–S Fuzzy Descriptor Systems With Structured Parametric Uncertainties

This article considers admissibility analysis and robust ${H_\infty }$ control for continuous-time Takagi–Sugeno fuzzy descriptor systems with norm-bounded uncertainties in all parametric matrices. The system under consideration contains singular derivative matrices and different membership functions, thus it generalizes other related forms. First, uncertainties in derivative matrices are divided into two cases, i.e., one is expressed by a constant matrix left multiplied by an invertible uncertain matrix and the other is produced by its dual form. Then, admissible conditions and ${H_\infty }$ performance for the system with the first case of uncertainties are derived based on a new augmented system. As for the second case, the admissibility analysis is converted into the first case by an equivalent companion system then solved as well. All conditions are cast into strict linear matrix inequalities. Besides, due to the introduction of a new nonquadratic fuzzy Lyapunov function and slack decision variables, the proposed methods are less conservative than related ones. Finally, simulation examples are provided to illustrate improvements and effectiveness of the main results.

Robust H∞ sliding mode observer design for a class of Takagi–Sugeno fuzzy descriptor systems with time-varying delay

This paper focuses on the problem of robust H∞ sliding mode observer (SMO) design for a class of Takagi–Sugeno (T–S) fuzzy descriptor systems with time-varying delay. A SMO is designed by taking the control input and the measured output into account. Then a novel integral-type sliding surface, which involves the SMO gain matrix, is constructed for the error system. By using an appropriate Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamic to be robustly admissible with H∞ performance and determines the SMO gain matrix. Moreover, a sliding mode control (SMC) law is synthesized such that the reachability can be ensured. Finally, simulations are presented to show the effectiveness of our results.

Admissibility Analysis and Control Synthesis for T–S Fuzzy Descriptor Systems

The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.

Robust stabilizing controller design for Takagi–Sugeno fuzzy descriptor systems under state constraints and actuator saturation

The aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by Takagi–Sugeno fuzzy descriptor systems and subject to input and state constraints. For this, a novel structure of modified parallel distributed compensation control laws is proposed. The controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from Lyapunov's stability theory and the choice of an original Lyapunov function. This ensures the stabilization of the closed-loop system and the respect of the state and input constraints regionally. The technique is illustrated through three numerical examples.

An improved robust finite-time dissipative control for uncertain fuzzy descriptor systems with disturbance

ABSTRACTIn this paper, finite-time robust control problems are investigated for Takagi– Sugeno fuzzy descriptor systems. We provide a novel sufficient condition for robust finite-time admissibility of Takagi– Sugeno fuzzy descriptor systems, involving a group of coupled linear matrix inequalities (LMIs), which guarantee dissipative performance, reduce conservativeness and improve LMIs forms. Second, corresponding controllers are developed based on both parallel distributed compensation and non-parallel distributed compensation. Simulations demonstrate the effectiveness of the proposed control approach.

Fuzzy-model-based admissibility analysis for nonlinear discrete-time descriptor system with time-delay

This paper is concerned with the admissibility analysis problems of discrete-time Takagi–Sugeno fuzzy descriptor system with time-varying delay. The upper and lower bound of time-delay is assumed to be available online. By defining new Lyapunov functions and by making use of novel technique, delay dependence condition is given for the admissibility analysis of the systems without matrix decoupling and matrix transformation. The merit of the proposed conditions lies in their less conservativeness, which is achieved by combining some bounding inequalities for cross products between two vectors. Finally, these conditions are shown to be the effectiveness via two examples.

Fault Reconstruction and Fault-tolerant Control via Learning Observers in Takagi-Sugeno Fuzzy Descriptor Systems with Time Delays

This paper addresses the problems of observer-based fault reconstruction and fault-tolerant control for Takagi–Sugeno fuzzy descriptor systems subject to time delays and external disturbances. A novel fuzzy descriptor learning observer is constructed to achieve simultaneous reconstruction of system states and actuator faults. Sufficient conditions for the existence of the proposed observer are explicitly provided. Utilizing the reconstructed fault information, a reconfigurable fuzzy fault-tolerant controller based on the separation property is designed to compensate for the impact of actuator faults on system performance by stabilizing the closed-loop system. In addition, the design of the fault reconstruction observer and the fault-tolerant controller is formulated in terms of linear matrix inequalities that can be conveniently solved using convex optimization techniques. Finally, simulation results on a truck–trailer system are presented to verify the effectiveness of the proposed approaches.

Delay‐dependent dissipative control for a class of non‐linear system via Takagi–Sugeno fuzzy descriptor model with time delay

This paper studies the dissipative control problems for the non-linear descriptor system via a Takagi-Sugeno descriptor model with time delay and uncertainties. The considered systems are not necessarily regular or impulse free. Using the free-weighting-matrix approach combined with the developed linear matrix inequality techniques, the authors proposed an improved delay-dependent stability criterion to guarantee the system to be admissible. Based on this criterion, the solvable conditions for the existence of dissipative controller are derived, which guarantees that the closed-loop system is not only admissible but also strictly dissipative for all admissible uncertainties. The proposed method is more suitable for the robust stability analysis and control synthesis. Moreover, different control processes can be achieved for the targeted systems in the same design process. Therefore it could potentially reduce cost and time in the controller design for an actual physical system. The authors perform simulations to validate the obtained method for practical examples.

Passivity and passification of T–S fuzzy descriptor systems with stochastic perturbation and time delay

This study is concerned with the passivity and passification problems for Takagi–Sugeno fuzzy descriptor systems subject to stochastic perturbation and time-varying delay. The stochastic disturbance is given in the form of one-dimensional Brownian motion and the delay is assumed to be time-varying and differentiable. By utilising the Lyapunov functional method and the stochastic analysis techniques, a delay-dependent criterion is presented to ensure that the considered system is regular, impulse-free, asymptotically stable in the mean-square sense and passive in the sense of expectation. Then, based on this criterion, two procedures are proposed for designing state-feedback controller, which guarantee the resulting closed-loop system admissible and passive in the sense of expectation. All conditions are cast in terms of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the validity and applicability of the proposed results.

On dissipativity of Takagi–Sugeno fuzzy descriptor systems with time-delay

This paper is concerned with the dissipativity analysis for Takagi–Sugeno (T–S) fuzzy descriptor systems with time-delay. By using of delay partitioning approach, a delay-dependent criterion is established in terms of strict linear matrix inequalities (LMIs), which guarantees the considered system to be admissibility and strict (Q,R,S)-α-dissipativity. The obtained results dependent upon not only time delay but also the number of delay partitions, thus are less conservative. In addition, the developed results encompass available results on H∞ performance and strict passivity analysis as special cases. A numerical example is provided to illustrate the effectiveness of the proposed theories.