Passivity analysis for uncertain BAM neural networks with time delays and reaction–diffusions

This article deals with the problem of passivity analysis for delayed reaction–diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.     

Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

In this paper, the Takagi–Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Cohen–Grossberg type bidirectional associative memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by using LMI optimization algorithms to guarantee the asymptotic stability of uncertain Cohen–Grossberg BAM neural networks with time varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Finite-time stability analysis for fractional-order Cohen–Grossberg BAM neural networks with time delays

In this paper, the problem of finite-time stability for a class of fractional-order Cohen–Grossberg BAM neural networks with time delays is investigated. Using some inequality techniques, differential mean value theorem and contraction mapping principle, sufficient conditions are presented to ensure the finite-time stability of such fractional-order neural models. Finally, a numerical example and simulations are provided to demonstrate the effectiveness of the derived theoretical results.

     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Exponential H∞ stable learning method for Takagi–Sugeno fuzzy delayed neural networks: A convex optimization approach

In this paper, we propose some new results on stability for Takagi–Sugeno fuzzy delayed neural networks with a stable learning method. Based on the Lyapunov–Krasovskii approach, for the first time, a new learning method is presented to not only guarantee the exponential stability of Takagi–Sugeno fuzzy neural networks with time-delay, but also reduce the effect of external disturbance to a prescribed attenuation level. The proposed learning method can be obtained by solving a convex optimization problem which is represented in terms of a set of linear matrix inequalities (LMIs). An illustrative example is given to demonstrate the effectiveness of the proposed learning method.     

Analysis for Cohen-Grossberg neural networks with multiple delays

The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality （LMI） is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.     

Stabilization for Takagi–Sugeno fuzzy systems based on partitioning the range of fuzzy weights

In this note, the state-feedback stabilization for continuous-time Takagi–Sugeno (T–S) fuzzy systems is addressed, where the fuzzy weighting functions are assumed to be differentiable and their ranges of variation are possibly bounded by some parameters. By utilizing the matrix elimination lemma and introducing a polyhedral partition to the range of the fuzzy weights, the quadratically parameterized condition is transformed to being piecewise linear in both the fuzzy weights and their derivatives. Then, a switching control based on the partition is considered, by utilizing the extreme points in each partition to address the constraints of the fuzzy weights and their derivatives. The simulation shows that finer subdivision in the partition leads to better stability and stabilization margins.     

Stability analysis of fractional-order Cohen–Grossberg neural networks with time delay

In this paper, the existence and finite-time stability of equilibrium point for a class fractional-order Cohen–Grossberg neural networks with time delay are investigated. Moreover, some sufficient conditions for the finite time stability are obtained by using Bellman–Gronwall inequality and differential mean value theorem,and contraction mapping. Finally, an example is given to illustrate the effectiveness of the results.     

Stability analysis and design of fuzzy control system with bounded uncertain delays

Fuzzy control problems for systems with bounded uncertain delays were studied. Based on Lyapunov stability theory and matrix theory, a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities （LMI） approach, and the global exponential stability of the closed-loop system was strictly proved. For a fuzzy control system with bounded uncertain delays, under the global exponential stability condition which is reduced to p linear matrix inequalities, the controller guarantees stability performances of state variables. Finally, the simulation shows the validity of the method in tiffs paper.     

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.     

Fault reconstruction for Takagi–Sugeno fuzzy systems via learning observers

This paper addresses the problem of observer-based fault reconstruction for Takagi–Sugeno fuzzy systems. Two types of fuzzy learning observers are constructed to achieve simultaneous reconstruction of system states and actuator faults. Stability and convergence of the proposed observers are proved using Lyapunov stability theory, and necessary conditions for the existence of the observers are further discussed. The design of fuzzy learning observers can be formulated in terms of a series of linear matrix inequalities that can be conveniently solved using convex optimisation technique. A single-link flexible manipulator is employed to verify the effectiveness of the proposed fault-reconstructing approaches.     

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.     

Non-chattering quantized control for synchronization in finite–fixed time of delayed Cohen–Grossberg-type fuzzy neural networks with discontinuous activation

Neural Computing and Applications - This paper investigates the controller design problem of synchronization in finite- $$setminus $$ fixed-time of a class Cohen–Grossberg-type fuzzy neural...     

Global exponential stability analysis of cellular neural networks with multiple time delays

Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.     

On reducing computational overhead in multi-objective genetic Takagi–Sugeno fuzzy systems

The use of multi-objective evolutionary algorithms (MOEAs) to generate a set of fuzzy rule-based systems (FRBSs) with different trade-offs between complexity and accuracy has gained more and more interest in the scientific community. The evolutionary process requires, however, a large number of FRBS generations and evaluations. When we deal with high dimensional datasets, these tasks can be very time-consuming, especially when we generate Takagi–Sugeno FRBSs, thus making a satisfactory exploration of the search space very awkward. In this paper, we first analyze the time complexity for both the generation and the evaluation of Takagi–Sugeno FRBSs. Then we introduce a simple but effective technique for speeding up the identification of the rule consequent parameters, one of the most time-consuming phases in Takagi–Sugeno FRBS generation. Finally, we highlight how the application of this technique produces as a side-effect a decoupling of the rules. This decoupling allows us to avoid re-computing consequent parameters of rules which are not directly modified during the evolutionary process, thus saving a considerable amount of time.In the experimental part we first test the correctness of the predicted asymptotical time complexity. Then we show the benefits in terms of computing time saving and improved search space exploration through an example of multi-objective genetic learning of Takagi–Sugeno FRBSs in the regression domain.     

A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi–Sugeno fuzzy systems

This paper deals with stability analysis and control design problems for continuous-time Takagi–Sugeno (T–S) fuzzy systems. The first aim is to present less conservative linear matrix inequality (LMI) conditions to design controllers and assess the stability. The second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction (DA) via LMIs. The results are based on the fuzzy Lyapunov functions (FLFs) and non-parallel distributed compensation (non-PDC) approaches. Finally, examples illustrate the effectiveness and merits of the proposed methods.