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New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

This paper presents a novel framework for designing a super-twisting algorithm-based fuzzy sliding mode controller to address critical challenges in descriptor T-S fuzzy systems. First, an innovative integral-type sliding surface is proposed, eliminating the longstanding requirement for prior knowledge concerning the derivatives of membership functions (MFs)-a key limitation in existing methods. This approach constitutes a significant advance, ensuring asymptotic stability of the sliding motion without restrictive assumptions on MF dynamics. Subsequently, a multivariable super-twisting algorithm is developed specifically for descriptor T-S systems. This development fundamentally ensures continuity of the closed-loop states and suppresses chattering by design. Finally, two examples are numerically simulated to test the validity of the method proposed.

This paper addresses the problems of the robust stability and stabilization for fractional order systems based on uncertain Takagi–Sugeno fuzzy model. A sufficient condition of asymptotical stability for fractional order uncertain T–S fuzzy model is given, and a parallel distributed compensating fuzzy controller is designed to asymptotically stabilize the model. The sufficient conditions are formulated in the format of linear matrix inequalities. The fractional order T–S fuzzy model of a chaotic system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the approach is tested on fractional order Rössler system and fractional order uncertain Lorenz system.

To improve the transient performance of speed tracking control while ensuring stability and considering actuator constraints in heavy-haul train systems, this paper proposes a novel cruise control method based on a nonparallel distributed compensation (non-PDC) fuzzy-based composite nonlinear feedback (CNF) technique. First, a low-dimensional nonlinear multi-particle error dynamics model is established based on the fencing concept, simplifying the model significantly. To facilitate controller design, a Takagi–Sugeno (T-S) fuzzy model is derived from the nonlinear model. Subsequently, sufficient conditions for the non-PDC fuzzy-based CNF controller are provided in terms of linear matrix inequalities (LMIs), with the controller design addressing asymmetric constraints on control inputs due to differing maximums of traction and braking forces. Simulations based on MATLAB/Simulink are conducted under different maneuvers to validate the effectiveness and superiority of the proposed method. The simulation results demonstrate a notable enhancement in transient performance (over 22.3% improvement in settling time) and steady-state cruise control performance for heavy-haul trains using the proposed strategy.

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T–S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T–S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T–S fuzzy hyperbolic model with the discrete T–S fuzzy linear one are also given to illustrate the advantage of our approach.

Less conservative condition is provided in this paper for quadratic stabilization of guaranteed cost control (GCC) of Takagi–Sugeno fuzzy systems with parallel distributed compensation (PDC). To derive the condition, firstly a parameter-dependent linear matrix inequality (PD-LMI) is established to find quadratically stable PDC controller gains of GCC. Secondly, by applying Pólya’s theorem, evaluation of the PD-LMI is transformed into an equivalent problem of evaluation of a sequence of LMI relaxations. Different from other existing conditions, the LMI relaxations are sufficient and asymptotically reach necessity for evaluating the PD-LMI as a related scalar parameter, d, increases. The resulting guaranteed costs of PDC controllers are non-increasing with respect to the increase in the parameter d and converge to the global optimal value under quadratic stability at the limiting case. In addition, for input-affine nonlinear systems, the proposed condition is extended with the consideration of modeling errors, which helps to reduce the computational complexity of the LMI relaxations. Finally, simulations of two examples demonstrate the efficiency and feasibility of the proposed condition.

The paper presents a robust parallel distributed compensation (PDC) fuzzy controller for a nonlinear and certain system in continuous time described by the Takagi-Sugeno (T-S) fuzzy model. This controller is based on a new type of time-varying fuzzy sets (TVFS). These fuzzy sets are characterized by displacement of the kernels to the right or left of the universe of discourse, and they are directed by a well-defined criterion. In this work, we only focused on the movement of midpoint of the universe. The movements of this midpoint are optimized by particle swarm optimization (PSO) approach.

Pressure ripples in electric power steering (EPS) systems can be caused by the phase lag between the driver’s steering torque and steer angle, the nonlinear frictions, and the disturbances from road and sensor noise especially during high-frequency maneuvers. This paper investigates the use of the robust fuzzy control method for actively reducing pressure ripples for EPS systems. Remarkable progress on steering maneuverability is achieved. The EPS dynamics is described with an eight-order nonlinear state-space model and approximated by a Takagi-Sugeno (T-S) fuzzy model with time-varying delays and external disturbances. A stabilization approach is then presented for nonlinear time-delay systems through fuzzy state feedback controller in parallel distributed compensation (PDC) structure. The closed-loop stability conditions of EPS system with the fuzzy controller are parameterized in terms of the linear matrix inequality (LMI) problem. Simulations and experiments using the proposed robust fuzzy controller and traditional PID controller have been carried out for EPS systems. Both the simulation and experiment results show that the proposed fuzzy controller can reduce the torque ripples and allow us to have a good steering feeling and stable driving.

In this paper, the descriptor system based concept is applied to the stabilization for a discrete T-S fuzzy system. The control input vector and state vector are combined to the descriptor system form which leads to fewer Lyapunov inequalities (lower computation demand) than traditional T-S fuzzy stability criteria. Also, the non-parallel distributed compensation (non-PDC) and slack variables are adapted to relax the proposed stability conditions. Finally, the computation effectiveness the proposed stability criterion is demonstrated by a numerical example.

The design of a model-free fuzzy power system stabilizer (PSS) lacks systematic stability analysis and performance guarantees. This paper provides a step toward the design of a model-based fuzzy PSS that guarantees not only robust stability but also robust performance of power systems. A new practical and simple design based on dynamic output feedback is proposed. The design model is approximated by a set of Takagi-Sugeno (T-S) fuzzy models to account for nonlinearities and uncertainties. The proposed stabilizer is based on parallel distributed compensation (PDC). Sufficient design conditions are presented as linear matrix inequalities (LMIs). The design procedure leads to a tractable convex optimization problem in terms of the stabilizer gain matrices. The design guarantees robust pole clustering, in an acceptable region in the open left half of the complex plane, and robust performance in terms of H2 and H∞ measures, over a wide range of operating conditions. Simulations results of both single-machine and multi-machine power systems confirm the effectiveness of the proposed PSS design.