Stability analysis of uncertain neutral systems with discrete and distributed delays via the delay partition approach

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.     

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

The problem of non‐fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time‐delay signals is investigated in this paper. By constructing a suitable Lyapunov‐Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay‐dependent non‐fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non‐fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non‐fragile state feedback controller is designed for GNNs such that the closed‐loop system is extended dissiptive. Thus, the non‐fragile extended dissipative controller can be adopted to deal with the non‐fragile performance, non‐fragile performance, non‐fragile passive performance, non‐fragile mixed and passivity performance, and non‐fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real‐life application of the quadruple tank process system.     

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

This paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.     

Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality

This paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval time‐varying delays. Different from previous literature, some sufficient information on a complex‐valued neuron activation function and interval time‐varying delays has been considered into the record. A suitable Lyapunov‐Krasovskii functional with some delay‐dependent terms is constructed. By applying modern integral inequalities, several sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed system model. All the proposed criteria are formulated in the structure of a complex‐valued linear matrix inequalities technique, which can be checked effortlessly by applying the YALMIP toolbox in MATLAB linear matrix inequality. Finally, two numerical examples with simulation results have been provided to demonstrate the efficiency of the proposed method.     

Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays

This paper is concerned with the passivity analysis problem for a class of discrete-time stochastic bidirectional associative memory neural networks with time-varying delays. Furthermore, the results are extended to the robust passivity analysis with mixed time delays that consist of both the discrete and distributed time delays, and the uncertainties are assumed to be time-varying norm bounded parameter uncertainties. By constructing a new Lyapunov–Krasovskii functional and introducing some appropriate free-weighting matrices, a delay-dependent passivity criterion is derived in terms of LMIs whose feasibility can be easily checked by some available software packages. Finally, two numerical examples with simulation results are given to demonstrate the effectiveness and usefulness of the proposed results.     

Stability and dissipativity analysis for uncertain Markovian jump systems with random delays via new approach

This paper studies the problem of stability and dissipativity analysis for uncertain Markovian jump systems (UMJSs) with random time-varying delays. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical tools, a new double integral inequality (NDII) is developed. Then, to show the efficiency of the proposed inequality, a suitable Lyapunov-Krasovskii functional (LKF) is constructed with augmented delay-dependent terms. By employing integral inequalities, new delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness and less conservatism of the results.     

Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay

The objective of this paper is to analyze the stability analysis of neutral-type neural networks with additive time-varying delay and leakage delay. By constructing a suitable augmented Lyapunov-Krasovskii functional with triple and four integral terms, some new stability criteria are established in terms of linear matrix inequalities, which is easily solved by various convex optimization techniques. More information of the lower and upper delay bounds of time-varying delays are used to derive the stability criteria, which can lead less conservative results. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasible can be checked easily by MATLAB LMI control toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.