Fuzzy Delta Operator Systems Research Articles

Memory-based passive control design for complex networked fuzzy delta operator systems

This article investigates the memory-based state-feedback control with strict passivity performance for nonlinear systems in delta domain. Takagi–Sugeno fuzzy model of delta operator form is adopted as an approximator of the investigated nonlinear plant with system perturbations/exogenous disturbances. The nonlinear output of the plant, which is accompanied with complex exogenous disturbances, is formulated as the passive output satisfying a pre-designed strict passivity performance. The memory-based state-feedback controller is expressed with a known memory coefficient to significant the influence of the delayed states. The resulting closed-loop system is inferred as a time-varying delay system, of which the stability and passivity criterion is carried out via a general fuzzy Lyapunov–Krasovskii functional approach. Then, parametric gains of the desired strictly passive memory-based controller are designed subject to a set of solvable matrix inequalities. Finally, a numerical example shows the validity of the proposed memory-based passive control method.

Output-Feedback Control for T–S Fuzzy Delta Operator Systems With Time-Varying Delays via an Input–Output Approach

In this paper, the problem of induced L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> disturbance attenuation control is investigated for discrete-time Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delays and disturbance input via an input-output approach. A model transformation method is utilized to approximate the time-varying delay in T-S fuzzy delta operator systems. By applying the scaled small gain (SSG) theorem and Lyapunov-Krasovskii functional approach, a sufficient condition is established to guarantee that the closed-loop system is asymptotically stable and has an induced L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> disturbance attenuation performance. The existence condition of the dynamic output-feedback controller can be solved via convex optimization problems. Finally, simulation results are given to demonstrate the feasibility and effectiveness of the proposed method.

Output tracking control for fuzzy delta operator systems with time-varying delays

This paper addresses the fuzzy output tracking control problem of Takagi–Sugeno (T–S) fuzzy delta operator systems with time-varying delays. For a new model transformation, the time-varying delay is approximated via an input–output approach. Based on the transformed model, a sufficient criterion of asymptotic stability with H∞ tracking performance is derived for the closed-loop system by using scaled small gain theorem. Based on the criterion, a fuzzy H∞ state-feedback controller is designed such that the output of the plant can track the output of a given reference model in H∞ sense. The existence condition of the controller can be expressed by a convex optimization problem. Finally, simulation results are given to demonstrate the effectiveness and potential of the proposed new design technique.

Robust fuzzy-scheduling control for nonlinear systems subject to actuator saturation via delta operator approach

This paper focuses on robust fuzzy-scheduling control for nonlinear systems with actuation saturation via delta operator approach. A class of T–S fuzzy delta operator systems is extended to describe nonlinear systems subject to actuator saturation and linear fractional uncertainty. Moreover, a set invariance condition is established for T–S fuzzy delta operator systems. Based on the set invariance condition, an optimization approach is proposed to estimate the domain of attraction for the T–S fuzzy delta operator systems. The domain of attraction is arbitrarily close to a null controllable region by the designed PDC control law or non-PDC control law. Furthermore, the non-PDC control law is proposed by using fuzzy weighting-dependent Lyapunov function. The effectiveness of the developed techniques is shown through a numerical example.

Fault-tolerant control for a class of T–S fuzzy systems via delta operator approach

This paper studies a fault-tolerant control scheme for T–S fuzzy models based on delta operator approach. A fuzzy fault detection observer is constructed by means of T–S fuzzy delta operator systems. Moreover, a new approach is established for the estimation of faults in a class of nonlinear systems. The proposed fault-detection observer can be obtained in terms of the solvability of linear matrix inequalities. Then, an active fault-tolerant controller is designed to compensate for the effect of the faults and makes the closed-loop fuzzy delta operator system stable. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.

Fault Detection for Uncertain Fuzzy Systems Based on the Delta Operator Approach

This paper investigates the problem of designing a robust fault-detection for uncertain T-S fuzzy models based on the delta operator approach. By means of the T-S fuzzy delta operator systems, a fuzzy fault detection filter system is constructed via the delta operator approach. The worst case fault sensitivity has been formulated in terms of linear matrix inequalities. The proposed fault-detection filter not only ensures the H −-gain from a fault signal to a residual signal greater than a prescribed value, but also guarantees the H ∞-gain from an exogenous input to a residual signal less than a prescribed value in terms of the solvability of linear matrix inequalities. The linear matrix inequalities can be solved by an effective algorithm. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.

Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.

Robust H∞ control for a class of discrete time fuzzy systems via delta operator approach

In this paper, we investigate a robust H ∞ control problem for a class of T–S fuzzy systems with time delays by using delta operator approach. It is known that a better control effect can be obtained by using delta operator approach than using shift operator approach for small sampling periods. Furthermore, the delta operator can unify some previous related continuous and discrete fuzzy systems into fuzzy delta operator system framework. Based on Lyapunov–Krasovskii functionals in delta domain, a new fuzzy H ∞ state feedback controller is presented in terms of linear matrix inequalities. Some experiment results of an ball and beam model on a laboratory-scale setup are presented to illustrate the effectiveness and potential for the developed techniques.