Fuzzy Time Delay Research Articles

Output Switching Control of a Class of Time-Delay Fuzzy Systems

For a class of T-S fuzzy time-delay systems, the problem of designing a static output feedback controller is considered via the parallel distributed compensation (PDC) approach. Namely, when one controller can not assure the stability of system, a controller switching strategy in certain set of controllers may stabilize the system. Moreover the adoption of this strategy often improves the performance of system even in the case that a single controller can stabilize the system. By defining multiple Lyapunov functions, the sufficient condition for the existence of the static out put feedback controller is presented in terms of linear matrix inequality (LMI), which guarantees the stability of the close-loop system for the switching cases. The simulation results demonstrate the effectiveness of the proposed method.

Stability analysis and decentralized H∞ control for time-delay fuzzy interconnected systems via fuzzy Lyapunov-Krasovskii functional

This paper is concerned with the stability analysis and H∞ fuzzy controller design of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of N interconnected time-delay Takagi-SugenoT-S fuzzy subsystems and the delay-dependent stability analysis is based on the fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is shown that the delay-dependent stability of the time-delay fuzzy interconnected systems can be established if a fuzzy weighting-dependent Lyapunov-Krasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities LMIs that are numerically feasible. The decentralized H∞ controllers are also designed by solving a set of LMIs based on these fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is demonstrated via numerical examples that the stability and controller synthesis results based on fuzzy weighting-dependent Lyapunov-Krasovskii functionals are less conservative than those based on the common quadratic Lyapunov-Krasovskii functionals.

New delay dependent robust stability criteria for T-S fuzzy systems with constant delay

This paper deals with the problem of delay dependent robust stability for T-S fuzzy time delay systems. The approach based on constructing a new Lyapunov-Krasovskii functional by dividing uniformly the delay interval into N segment with N is positive integer, and using Finsler’s lemma. This new Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments. The perturbations considered are norm bounded, and the results are expressed in terms of linear matrix inequality (LMIs). Numerical examples are provided to show the effectiveness of the present method, compared with some recent previous ones.

New Approach to Delay-Dependent Control for Fuzzy Time-Delay Systems

A new control method is proposed for stability analysis and stabilization problems for T-S fuzzy systems with time-delay. A new fuzzy Lyapunov-Krasovskii functional is introduced to establish some delay-dependent stability criteria. Based on parallel distributed compensation (PDC) scheme, a delay-dependent stabilization condition is derived and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples show that the effectiveness and benefits of the proposed method.

Recurrent Fuzzy-Neural MIMO Channel Modeling

Fuzzy systems and artificial neural networks (ANN), as important components of soft-computation, can be applied together to model uncertainty. A composite block of the fuzzy system and the ANN shares a mutually beneficial association resulting in enhanced performance with smaller networks. It makes them suitable for application with time-varying multi-input multi-output (MIMO) channel modeling enabling such a system to track minute variations in propagation conditions. Here we propose a fuzzy neural system (FNS) using a fuzzy time delay fully recurrent neural network (FTDFRNN) that has the capability to tackle time-varying inputs in fuzzified form and is used to model MIMO channels. The inference engine is constituted by novel FTDFRNN blocks which determine the decision boundaries and tracks in-phase and quadrature components of input signals encompassing stochastic behavior of the MIMO channel. The system shows significant improvement in performance compared to statistical and ANN approaches in terms of faster processing time, lower bit error rate (BER) margins and better precision while carrying out symbol recovery of transmitted data through severely faded MIMO channels.

Train Timetable Problem on a Single-Line Railway With Fuzzy Passenger Demand

The aim of the train timetable problem is to determine arrival and departure times at each station so that no collisions will happen between different trains and the resources can be utilized effectively. Due to uncertainty of real systems, train timetables have to be made under an uncertain environment under most circumstances. This paper mainly investigates a passenger train timetable problem with fuzzy passenger demand on a single-line railway in which two objectives, i.e., fuzzy total passengers' time and total delay time, are considered. As a result, an expected value goal-programming model is constructed for the problem. A branch-and-bound algorithm based on the fuzzy simulation is designed in order to obtain an optimal solution. Finally, some numerical experiments are given to show applications of the model and the algorithm.

Robust Η-infinity Fuzzy Control for a Class of Time-Delay Fuzzy Bilinear Systems with an Additive Disturbance

Robust Η-infinity Fuzzy Control for a Class of Time-Delay Fuzzy Bilinear Systems with an Additive Disturbance

Stabilization of Networked Stochastic Time-Delay Fuzzy Systems With Data Dropout

This paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout. The plant in the networked control system (NCS) under consideration is a discrete stochastic time-delay nonlinear system represented by a Takagi-Sugeno fuzzy model. Exponential stability criteria of the NCS are developed by using a common quadratic Lyapunov function and a fuzzy Lyapunov function, respectively. A stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software. Three numerical examples are presented to demonstrate the effectiveness of the proposed methods.

Computational Effective Stability Conditions for Time-delay Fuzzy Systems

This paper investigates the system stability of the time-delay fuzzy-model-based control systems based on delay-independent and -dependent approaches. LMI-based delay-independent and -dependent stability conditions are derived to guarantee the system stability using Lyapunov-based technique. It can be seen that some existing stability analysis approaches require high computational demand to solve the solution due to the large number of stability conditions. Consequently, feasible solution may not be obtained with the use of numerical methods due to the limitation of the computer system especially for complicated fuzzy systems with a large number of rules. In this paper, under a particular system formulation, the number of stability conditions can be reduced to alleviate the computational demand on searching for the solution. Furthermore, the stability conditions offer a larger upper bound of time delay compared with some existing approaches. LMI-based performance conditions are also derived to guarantee the system performance. Simulation examples are given to illustrate the merits of the proposed approaches.

Fuzzy Guaranteed Cost Control for Fuzzy Time Delay Systems

Abstract Based on T-S fuzzy model, the guaranteed cost control problem of a class of uncertain nonlinear systems with input and state time delay is discussed. By constructing state-feedback controller, a sufficient condition that for the given performance index and control law, the closed-loop system is quadratic guaranteed cost stable is presented and expressed in terms of linear matrix inequality (LMI). A numerical example shows that the proposed design method is effective.

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

Fuzzy Time-Delay Systems and Their Stability

Fuzzy Time-Delay Systems and Their Stability

A SINGLE MACHINE SCHEDULING PROBLEM WITH FUZZY TIME DELAYS

An n+1 jobs single machine problem with fuzzy time delays is considered. Fuzzy time delay means the time between the completion of a job and the beginning of any of its predecessors, which must be within prescribed limits. A special fuzzy delays structure is investigated, which time delay only occur between Ji ( i = 1, 2, …, n) and Jn+1. Optimal solutions for the scheduling model under several cases are developed.

Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.

A Stability Criterion of Time-Delay Fuzzy Systems

To guarantee the asymptotic stability, a stability criterion in terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems is proposed in this paper. Each of these systems consists of a number of subsystems represented by Takagi-Sugeno fuzzy models with multiple time delays.