Zhiguang Feng

Exponential Stability Analysis for Delayed Neural Networks With Switching Parameters: Average Dwell Time Approach

This paper is concerned with the problem of exponential stability analysis of continuous-time switched delayed neural networks. By using the average dwell time approach together with the piecewise Lyapunov function technique and by combining a novel Lyapunov-Krasovskii functional, which benefits from the delay partitioning method, with the free-weighting matrix technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time-varying delays, respectively. Moreover, the decay estimates are explicitly given. The results reported in this paper not only depend upon the delay but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results.

Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks

In this brief, the problems of delay-dependent stability analysis and strict (Q,S,ℜ)-α-dissipativity analysis are investigated for cellular neural networks (CNNs) with distributed delay. First, by introducing an integral partitioning technique, two new forms of Lyapunov-Krasovskii functionals are constructed, and improved distributed delay-dependent stability conditions are established in terms of linear matrix inequalities. Based on this criterion, a new sufficient delay and α-dependent condition is given to guarantee that the CNNs with distributed delay are strictly (Q,S,ℜ)-α-dissipative. The results developed in this brief can tolerate larger allowable delay than existing ones in the literature, which is demonstrated by several examples.

Stability and Synchronization of Discrete-Time Neural Networks With Switching Parameters and Time-Varying Delays

This paper is concerned with the problems of exponential stability analysis and synchronization of discrete-time switched delayed neural networks. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time-delays. Benefitting from the delay partitioning method and the free-weighting matrix technique, the conservatism of the obtained results is reduced. In addition, the decay estimates are explicitly given and the synchronization problem is solved. The results reported in this paper not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results.

Robust reliable dissipative filtering for discrete delay singular systems

This paper is concerned with the problem of robust reliable dissipative filtering for uncertain discrete-time singular system with interval time-varying delay and sensor failures. The uncertainty and the sensor failures considered are polytopic uncertainty and varying in a given interval, respectively. The purpose is to design a filter such that the filtering error singular system is regular, causal, asymptotically stable and strictly (Q,S,R)-dissipative. By utilizing reciprocally convex approach, firstly, sufficient reliable dissipativity analysis condition is established in terms of linear matrix inequalities (LMIs) for singular systems with time-varying delay and sensor failures. Based on this criterion, the result is extended to uncertain singular systems with time-varying delay and sensor failures. Moreover, the reliable dissipative filter is designed in terms of linear matrix inequalities (LMIs) for uncertain singular systems with time-varying delay and sensor failures. Finally, the effectiveness of the filter design method in this paper is illustrated by numerical examples.

On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay

In this brief, the problem of extended dissipativity analysis for discrete-time neural networks with time-varying delay is investigated. The definition of extended dissipativity of discrete-time neural networks is proposed, which unifies several performance measures, such as the H∞ performance, passivity, l2-l∞ performance, and dissipativity. By introducing a triple-summable term in Lyapunov function, the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term and then the extended dissipativity criterion for discrete-time neural networks with time-varying delay is established. The derived condition guarantees not only the extended dissipativity but also the stability of the neural networks. Two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results.

Improved Stability Condition for Takagi–Sugeno Fuzzy Systems With Time-Varying Delay

In this paper, the stability analysis problem of Takagi–Sugeno fuzzy systems with time-varying delay is investigated. By utilizing the Wirtinger-based integral inequality and the improved reciprocally convex combination technique, an improved stability condition is derived in terms of linear matrix inequalities. A numerical example is given to demonstrate the efficiency of the obtained result.In this paper, the stability analysis problem of Takagi-Sugeno fuzzy systems with time-varying delay is investigated. By utilizing the Wirtinger-based integral inequality and the improved reciprocally convex combination technique, an improved stability condition is derived in terms of linear matrix inequalities. A numerical example is given to demonstrate the efficiency of the obtained result.

Dissipative control for linear systems by static output feedback

In this article, the problem of static output-feedback dissipative control is investigated for linear continuous-time system based on an augmented system approach. A necessary and sufficient condition for stability and strict (Q,S,R)-dissipativity of the closed-loop system is established in terms of a matrix inequality with free parametrisation matrix. An equivalent characterisation with some slack matrices for numerical solvability is then proposed. Based on this, a necessary and sufficient condition for the existence of a desired controller is given, and a corresponding iterative algorithm is developed to solve the condition. The effectiveness of results developed in this article is demonstrated by some numerical examples.

Reachable Set Estimation of T–S Fuzzy Systems With Time-Varying Delay

In this paper, the reachable set estimation problem is investigated for delayed discrete-time Takagi–Sugeno fuzzy systems with bounded input disturbances and nonzero initial conditions. A reachable set estimation condition is derived by using the reciprocally convex combination approach to bound the forward difference of triple-summable terms. The derived condition guarantees that all the states of the system with the initial conditions from some domain are bounded in a compact set, and all the states from other domain converge exponentially within another compact set. Moreover, a less conservative stability condition is also obtained. The effectiveness and the reduced conservatism of the proposed results are illustrated by numerical examples.

Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling

This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.

Improved stability and stabilization results for discrete singular delay systems via delay partitioning

In this paper, the problems of delay-dependent robust stability analysis and robust stabilization are investigated for uncertain discrete-time singular systems with state delay. First, by making use of the delay partitioning technique, a new delay-dependent criterion is given to ensure the nominal system to be regular, causal and stable. This new criterion is further extended to singular systems with both delay and parameter uncertainties. Moreover, without the assumption that the considered systems being regular and causal, robust controllers are designed for discrete-time singular time-delay systems such that the closed-loop systems have the characteristics of regularity, causality and asymptotic stability. These results are illustrated, via a few numerical examples, to be much less conservative than most of the existing results in the literature.