Stability Of Takagi-Sugeno Fuzzy Systems Research Articles

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation are investigated in this paper. Different from the existing quadratic event-triggered mechanism (ETM), a linear ETM is constructed, which can be reduced to a time-triggered mechanism (TTM). Based on parallel distribution compensation, an event-triggered fuzzy controller is designed, and sufficient conditions under the estimation of a certain domain of attraction are proposed to ensure the ETM-based and TTM-based closed-loop systems are positive and stable. The controller gain is solved directly by the proposed conditions. And then these sufficient conditions are extended to the conditions under the estimation of the largest domain of attraction by establishing an optimization problem. Furthermore, the linear ETM is proved to exclude the Zeno behavior of the system. Finally, two simulation examples are utilized to verify the effectiveness of the proposed event-triggered control scheme.

Enhanced Switching Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems: Reducing the Conservatism and Alleviating the Online Computational Burden

This article proposes an enhanced switching stabilization of Takagi-Sugeno fuzzy systems by developing a new fuzzy switching controller. A distinctive feature of the proposed approach is the enhanced ability to utilize the updated information of the normalized fuzzy weighting functions at each sampling point. Compared with those recent results in the literature, two key performance indexes, i.e., reducing the conservatism and alleviating the online computational burden, can be improved together while the off-line computational burden increases as a tradeoff but is still affordable from the point of algorithmic complexity. As a result, the efficiency of fuzzy stabilization is enhanced and thus its scope of application can be enlarged much more than before. Finally, the superiority of the proposed approach is illustrated by some simulation comparisons.

On the Uniform Stabilization of Takagi-Sugeno Fuzzy Systems with Uncertainties

This paper studies the stabilization based controller problem for Takagi-Sugeno fuzzy nonlinear systems. We give some new conditions to prove the global uniform stability of the closed-loop fuzzy control systems in presence of uncertainties. Furthermore, a numerical example is treated to validate our approach.

Improved criteria for the stabilization of T-S fuzzy systems with actuator failures via a sampled-data fuzzy controller

This paper studies a problem of the sampled-data stabilization for Takagi-Sugeno fuzzy systems with actuator failures. An improved Lyapunov functional is constructed, which is dependent on the fuzzy membership functions FMFs and includes the sampling states with two sampling instants. A new integral term including the FMFs is introduced into this Lyapunov functional for the first time. Each term in this Lyapunov functional need not be positive, but it should be positive at sampling instants. The variation range of the FMFs is taken into account in dealing with the derivative of this Lyapunov functional as well. Then, improved stabilization criteria guaranteeing a larger sampling interval are obtained by applying the developed fuzzy controller. Simulation examples are given to illustrate the effectiveness and less conservatism of the proposed method.

Stability and Stabilization With Additive Freedom for Delayed Takagi–Sugeno Fuzzy Systems by Intermediary-Polynomial-Based Functions

This paper is devoted to the stability and stabilization for Takagi-Sugeno fuzzy systems with time-varying delays. First, an improved matrix inequality is presented to bound both strictly and nonstrictly proper rational functions, which is more general than the existing versions of reciprocally convex lemmas. Second, by suitable operations on parameter-dependent polynomial multiplied by state rate, a couple of novel intermediary-polynomial-based functions (IPFs) are developed in delay-product types. Benefitting from slack matrices of IPFs, a certain degree of flexibility is furnished. More importantly than that, by feat of adjustment of the variable parameter, the resulting conditions will be further endowed with additive freedom, which relaxes the feasible space in a distinctive manner. Third, by utilizing IPFs along with triple integrals, the stability criteria and the controller design approach are derived by some advanced integral inequalities. Resorting to elaborate construction of IPFs, the strengths of bounding techniques are sufficiently exploited, and the information on delay derivative is adequately reflected. Consequently, more desirable performances are achieved, while without excessive computational complexity. Finally, the effectiveness of the proposed methods is verified by numerical examples.

Robust reliable H∞ control for fuzzy systems with random delays and linear fractional uncertainties

This article studies the reliable robust stabilization problem for a class of uncertain Takagi–Sugeno (TS) fuzzy systems with time-varying delays. The delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form. By implementing a proper novel Lyapunov functional together with linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions is derived to guarantee the asymptotic stability of TS fuzzy system with a prescribed H∞ performance index. Further, a reliable robust H∞ control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain TS fuzzy system. Further, Schur complement and Jensen's integral inequality are used to simplify the derivation in the main results. The set of sufficient conditions is established using the relationship among the random time-varying delay and its lower and upper bounds, which can be easily solved by MATLAB LMI toolbox. Finally, an illustrative example based on the truck-trailer model is provided to show the effectiveness of the proposed new design technique.

Stability and Stabilization of Takagi-Sugeno Fuzzy Systems via Sampled-Data and State Quantized Controller

In this paper, we investigate the problem of stability and stabilization for sampled-data fuzzy systems with state quantization. By using an input delay approach, the sampled-data fuzzy systems with state quantization are transformed into a continuous-time system with a delay in the state. The transformed system contains nondifferentiable time-varying state delay. Based on some integral techniques, some new stability and stabilization criteria are first proposed by a modified Lyapunov functional. Furthermore, in the case of no quantization, some new stability and stabilization criteria are also obtained. It is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing ones in the literature. Two simulation examples are given to show the effectiveness of the proposed design method.

New stability method applied to the stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a new stability method previously developed and presented by the authors. The new stability method is here extended to fuzzy systems. In essence, the authors consider the stabilization of a fuzzy control system with parallel distributed compensation. This problem has been considered in detail previously by different authors using fuzzy Lyapunov function theory. However, in this paper the authors show that their new stability method presents a viable alternative to Lyapunov's method for such control systems. This statement is confirmed by a demonstration that the new stability method always provides necessary and sufficient conditions, the satisfaction of which guarantees that the system in question will be asymptotically stable.

On the Stability of Takagi–Sugeno Fuzzy Systems With Time-Varying Uncertainties

This paper studies the problems of stability analysis of Takagi-Sugeno free fuzzy systems with time-varying uncertainties. In our prior study, we represented the time-varying uncertainty incurred in characteristic interval matrices in terms of the stability of Takagi-Sugeno free fuzzy systems with consequent parameter uncertainties. Based on Mayer's convergent theorem for powers of single interval matrix and its generalization, we further proposed some sufficient conditions for the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be globally asymptotically stable. In this paper, we propose the notion of simultaneously nilpotent interval matrices to investigate the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be strongly stable within steps, where relates to the dimension of interval matrices. Moreover, a unique situation for the deterministic Takagi-Sugeno free fuzzy system to be strongly stable within steps is derived as well, where relates to the dimension of characteristic matrices for the deterministic Takagi-Sugeno free fuzzy system.

A multiple lyapunov function approach to stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.

Optimal Stabilization of Takagi-Sugeno Fuzzy Systems with Application to Spacecraft Control

We present a new design methodology for the optimal control of nonlinear systems described by the Takagi-Sugeno(TS) fuzzy model. After classifying the TS fuzzy systems into two families based on how diverse their input matrices are, controller synthesis procedure based on the inverse optimal design approach is given for each of these families. Also, it is shown that to find the parameters of the optimal controller can be represented as an LMI(linear matrix inequality) problem. Designed optimal controllers have the robustness with respect to certain input uncertainties. The proposed method is applied to a regulation problem of a rotating rigid spacecraft for verification.

Stability Analysis of Takagi-Sugeno Fuzzy Systems With Linear State-Space Submodels

This paper states a necessary condition for stability of Takagi-Sugeno fuzzy systems with linear state-space submodels in the consequents of rules. It is shown that in necessary contest the problem of stability analysis of Takagi-Sugeno fuzzy systems can be solved by testing robust stability of polynomials with polynomic structure of their coefficients. The robust stability of such polynomials is analyzed using modified criteria for stability test of polynomials with constant coefficients such as the Routh or the Jury table. Positivity of elements of these tables, which are polynomic functions of an interval parameter, is tested by Sign-decomposition. A necessary condition can be derived for both continuous-time and discrete-time systems.

Stability Analysis of Takagi-Sugeno Fuzzy Systems With Linear Input-Output Submodels: Polynomial Approach

The paper presents a necessary condition for stability of Takagi-Sugeno fuzzy systems with linear input-output submodels in the consequents of rules. The procedure can be performed for both continuous-time and discrete-time systems. The described procedure is based on converting of the initial problem into robust stability of uncertain systems. The robust stability analysis of systems with polynomic uncertainty of coefficients of their characteristic polynomials is tested using the Modified Routh or the Modified Jury criterion. These criteria enable to analyze the robust stability by testing positivity of multivariate polynomic functions. This step is performed using Bernstein algorithm - an efficient procedure decomposing an arbitrary polynomial to sum of polynomials of convenient properties.