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For the conservatism issue of state-feedback control for Takagi-Sugeno (T-S) fuzzy systems, a novel local controller design method and stability analysis approach are proposed in this article. First, based on a membership function piecewise linearization technique, a local linear controller is proposed to form a closed-loop system. Then, a series of system stability conditions are derived using quadratic and piecewise function approaches. Further, with a designed fuzzy local controller and fuzzy Lyapunov function, less conservative stability conditions are obtained. Finally, a simulation example is adopted to make comparisons with existing and proposed methods. The results clearly show the conservatism reduction and excellent performance of the proposed approach.

An integral sliding mode control method for uncertain Takagi–Sugeno fuzzy systems is investigated in this paper. Considering the time-varying property of the fuzzy system control matrix , a dimensional-varying integral sliding mode controller is proposed. With a membership function piecewise linearization technique, the gain matrices of equivalent control law are derived. Then a dimension switching sliding model control scheme is designed to close the control loop. As a result, traditional restrictions on input matrix can be further relaxed. Finally, a numerical and a Diesel Engine Air-Path control examples are provided to certificate the merits and effectiveness of the proposed approach.

For the problem of robust fault tolerant control of over-actuated nonlinear systems, a new robust synthesis method is investigated. The nonlinear system is modeled via a T–S fuzzy system approach with actuators layout. Based on a designed non-parallel distributed compensation form controller, the closed loop system is obtained. Then a more generalized performance index is introduced by involving the system transients and actuator faults. With a newly proposed nonlinear approximation method, a series of linear matrix inequalities which can make the system robust stable are listed. Finally, based on a dynamic positioning vessel control task, the validity of the proposed method is verified.

For Takagi–Sugeno (T–S) fuzzy systems, relaxed stability conditions are obtained by more effectively enveloping the trajectory of the membership functions (MFs) in a unified space of MF. Considering an open-loop T–S fuzzy system, the system premise variables operation domain can be divided into a series of subdomains. Based on an MF unified space extremum calculation technique, the MFs extremum values in each premise variable corresponding to the unified space subdomain are calculated. With these extremes, a tight local convex polyhedron enveloping the MF trajectory is constructed in each subdomain. Thus, linear matrix inequality (LMI) stability conditions are derived via a piecewise Lyapunov function. Then, a state-feedback local controller is designed to close the system loop. From a geometric viewpoint, MF extremum enveloping and piecewise linear-approximation methods are both utilized to achieve relaxed stability and robustness conditions. Finally, several examples are adopted to illustrate the metrics of the proposed approaches.

A functional observer–controller design problem of Takagi-Sugeno fuzzy systems with unmeasured premise variables and external disturbance is investigated in this paper. First, robust state feedback...

This paper studies reachable set estimation for systems with parameter uncertainties and known input. A new method is proposed for estimating real-time reachable sets of systems with parameter uncertainties, known input and non-zero initial condition. In order to reduce the effect of known inputs on the reachable set estimation, we propose a method by separating the uncertain systems into two subsystems: the subsystem with known input and the subsystem with parameter uncertainties. By solving the optimization problem in terms of linear matrix inequalities, real-time reachable sets are obtained. The effectiveness of the proposed method is illustrated by the simulation result of the lateral dynamic system of a vehicle.

For the output feedback control problem of a T‐S fuzzy system, an H∞ observer‐controller synthesis method is proposed. First, with parallel distributed compensation fuzzy observer and cont...

For the output feedback control problem of continuous-time T–S fuzzy systems with unknown premise variables, an H ∞ observer–controller design method in the low-frequency domain is proposed. First, an observer–controller structure is given, the unknown premise variables are limited by Lipschitz conditions. Then, the system stability conditions are obtained by the negativeness of eigenvalues' real parts. To achieve better control performance of the system in low frequency, the H ∞ index for attenuating the unknown low-frequency disturbance is guaranteed by generalised Kalman–Yakubovich–Popov lemma. Then, the stability and robustness conditions are converted into linear matrix inequality forms, which can be solved directly by a convex optimisation technique. Finally, several simulation examples carried out to show the effectiveness of the proposed method.

The paper is a study of quantized control for stochastic Markov jump systems with interval time-varying delays and bounded system noise under event-triggered mechanism. A new scheme of Lyapunov–Krasovskii functional which contains the quadratic terms and integral terms is presented. Then quadratic convex technology, the theory of stochastic switching system, and logarithmic quantizer are applied to this paper. The design of quantized controller is obtained with those methodologies. Different from previous results, our derivation applies the idea of second-order convex combination. The conservatism of stability criteria for systems is reduced by using this method. A numerical example under different conditions is given to demonstrate the effectiveness and validity of the new design techniques.

For the stability analysis of a polynomial fuzzy system, a new polynomial membership function approach is proposed to reduce conservatism. In this article, based on a state-feedback closed-loop system, a polynomials fitting method is utilized, and an improved membership function transformation technique is proposed to approximate the membership functions of the fuzzy system. Then, the membership-function-dependent polynomial-based stability conditions are derived. The obtained polynomial membership functions and approximation errors will be involved in the stability analysis process. Based on the sum-of-squares optimization technique, polynomial conditions can be directly solved. Finally, by several numerical and practical examples, conservatism reduction effects are shown by comparisons with existing methods.

For the stabilization problem of T-S fuzzy system, a new observer-based controller design approach is proposed when premise variables are not accessible. With a fuzzy observer, the estimated states error system is described as two parts: unknown premise variable caused terms and observer error terms. Consider the property that the norm of the unknown premise variable caused terms are under a Lipschitz condition constraint of observer error, an observer and controller errors augmented system is obtained. Then based on the Lyapunov function method, a series of linear matrix inequality conditions are proposed to asymptotically stabilize the system, the observer gain matrices are used to overcome the uncertainties caused by UPVs. Finally a simulation example is used to illustrate the effectiveness of the proposed method, comparisons with traditional method shows the conservatism reduction effects.

The observer-based controller design for a T–S fuzzy system subject to external disturbance is investigated in this paper. First, an $H_\infty$ observer is designed to estimate the unknown system states, by a transformation process for system states and the disturbance term, a state feedback $H_\infty$ controller is given. Then, the separation principle for a T–S fuzzy system subject to external disturbance is proposed. With the help of the improved separation principle, the observer and controller can be combined together to make the fuzzy system input-state stable, while the $H_\infty$ index can also be guaranteed. The proposed design approach is applicable for both known and unknown premise variables. In stability analysis, the membership functions derivatives dependent method is proposed to reduce the conservatism. In the simulation part, stability analysis of a three-rule system is carried out to illustrate the conservatism reduction effects in Example 1 ; then, a vessel dynamic positioning control process subject to ocean disturbance is adopted to illustrate the effectiveness of the proposed methods for both known/unknown premise variable cases.

In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.

To solve the state feedback stabilization problem for a class of T-S fuzzy systems, a new stability synthesis method is raised to further relax the conservatism existing in the analysis process. First, a series of nonlinear polynomials are used to approximate the system membership functions. And satisfied approximation results can be obtained. Then a polynomials transformation method is raised to change the polynomial membership functions into linear form. This method can facilitate the synthesis process and achieve better approximation precision. Therefore, by a membership function involving stability analysis approach, linear matrix inequality form stability conditions are given. Finally, by presenting and analyzing a numerical and a practical examples, the conservatism reduction effects of the proposed methods are verified.

Universalization, serialization and modularization are the three most important metrics in standardization of manufacturing. Developing with innovation of modern large-scale industrial production, a variety of methods were proposed to help enterprises to improve products’ applicability, prevent trade barriers, and promote technical cooperation. Meanwhile, some metrics were designed to evaluate or optimize these standardized procedures. However, no systematically quantitative model has been proposed to evaluate the standardization of equipment so far. In order to break the barrier, a quantitative analysis based evaluation model of equipment system is proposed in this paper, in which, universalization, serialization and modularization indices are defined based on heterogeneous information network. Comparing the results performed by the proposed model with experts’ evaluation, the metrics in proposed model can reveal the objective standardization of equipments.

With the advent of big data era, social media plays an important role in many areas such as security and finance. Researchers pay more attention on mining users’ interests through the social media data. A three-layer model (TLM) based on keyword extracting is proposed to mine users’ interests, which includes candidate words extracting, semantic structures analysing and interest words ranking. The TLM mainly focuses on both self-importance and semantic-importance of interest words. In addition, the TLM also considers the interest drifting to track long-term and short-term interests of users. Experiments conducted on 10 SINA Weibo datasets show that TLM is more efficient than existing methods to identify users’ interests based on hit rate.

The control problem of T-S fuzzy system with actuator amplitude, rate and acceleration saturations is addressed in this paper, where state augmented feedback controller with LMIs (Liner Matrix Inequalities) constraint conditions are proposed. Dynamic decoupling method is applied to fuzzify the input magnitude saturation nonlinearity into several sub-linear systems with fuzzy rules, thus a new T-S fuzzy system with input rate and acceleration saturations can be obtained. Then PDC (parallel distributed compensation) and NPDC (non-PDC) controller are both designed for the new T-S fuzzy system. The first and second order derivatives of input variable are given to obtain an augmented fuzzy system. As the augmented system output variable, the input rate is represented by first order derivative of the input term, the rate saturation constraint is described through norm bounded method. Moreover, the polytopic approach is used to replace the second order derivative of the input term, and a state augmented feedback NPDC controller is designed, the domain of attraction optimization process is also given. Finally, two practical examples are presented to show the effectiveness of proposed method.

This paper investigates the attitude coordinated tracking control for a group of rigid spacecraft under directed communication topology, in which inertia uncertainties, external disturbances, input saturation and constant time-delays between the formation members are handled. Initially, the nominal system with communication delays is studied. A delay-dependent controller is proposed by using Lyapunov–Krasovskii function and sufficient condition for system stability is derived. Then, an integral sliding manifold is designed and adaptive control approach is employed to deal with the total perturbation. Meanwhile, the boundary layer method is introduced to alleviate the unexpected chattering as system trajectories cross the switching surface. Finally, numerical simulation results are presented to validate the effectiveness and robustness of the proposed control strategy.