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In this paper, a robust H ∞ design approach is proposed to accomplish the state estimation task for a class of continuous-time gene regulatory networks (GRNs) in the finite-time framework. For the GRNs under investigation, the distributed inter-node time delays and intra-node time delays are, respectively, taken into account in the feedback regulation function and the translation process. Moreover, the parameter uncertainty with convex polytopic constraint is introduced to characterize the unavoidable modeling errors induced by parameter sensitivity, calibration accuracy, abrupt structural changes and failures, etc. The primary objective of this paper is to design a robust state estimator for the considered GRNs based on the measured concentrations of messenger ribonucleic acid and protein such that the finite-time boundedness and the H ∞ performance are guaranteed. By resorting to the Lyapunov stability theory, the Jensen's inequality and the Gronwall inequality, some sufficient conditions are established in terms of linear matrix inequalities. Subsequently, a set of parameter matrices with special structures is designed by means of the convex optimization techniques. Finally, a numerical example is provided to demonstrate the finite-time boundedness and the robust performance of the developed state estimation approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability issue of quaternion-valued neural networks with neutral delay, proportional delay and leakage delay. Taking use of the principle of homeomorphism, techniques of matrix inequality and Lyapunov stability theory, a main stability criterion is derived in the form of quaternion-valued linear matrix inequality for ensuring the unique existence and global stability of the equilibrium point for the considered quaternion-valued neural networks. An illustrative example and its simulations are given to show the effectiveness of the theoretical result. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the state estimation problem for a class of Markovian neural networks with discrete and distributed time-delays. The neural networks have a finite number of modes, and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally asymptotically stable in the mean square. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. Both the existence conditions and the explicit characterization of the desired estimator are derived. Furthermore, it is shown that the traditional stability analysis issue for delayed neural networks with Markovian jumping parameters can be included as a special case of our main results. Finally, numerical examples are given to illustrate the applicability of the proposed design method. [Copyright &y& Elsevier]

In this paper, a delay-dependent synchronization criteria for Markovian jump complex dynamical networks subject to time-varying coupling delays and external disturbances are proposed via Takagi-Sugeno (T-S) fuzzy approach. The class of Markovian jump complex dynamical networks is described by a fuzzy model composed of two levels such as a crisp level which represents the jumps and a fuzzy level which describes the system nonlinearities. An asymptotic synchronization criterion is obtained by employing fuzzy controller with the mixed H ∞ and passivity performance index ν > 0. Further, by constructing a novel Lyapunov-Krasovskii functional along with the extended integral inequality and using the properties of Kronecker product and convex combination approach, a set of sufficient constraints is derived in the form of linear matrix inequalities and checked for its feasibility using MATLAB software. At last, numerical simulations including the Lorentz system are given to demonstrate the applicability and effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of event-triggered non-fragile state estimator design for discrete-time delayed neural networks (DNNs) is investigated over finite-time span. In consideration of the changes of environment and high sensitivity, external disturbances and/or parameter uncertainties might be involved in estimator parameters of the concerned DNNs. Therefore, it is one of our main objectives to design a non-fragile state estimator subject to the norm bounded gain variation. The sensor nonlinearity is supposed to occur in a random way. In the meanwhile, the event-triggered scheme and energy constraints are adopted in state estimator design for the purpose of energy and resource saving. By using the Lyapunov stability theory and some analytical techniques, sufficient conditions are established to guarantee that the estimation error system is finite-time bounded and meet a prescribed mixed H ∞ and passivity performance constraint. Furthermore, the estimator gains are obtained via solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are exploited to demonstrate the effectiveness of the developed technique. [ABSTRACT FROM AUTHOR]

Abstract This paper focus on the synchronization of complex-valued neural networks (CVNNs) with both discrete and distributed two additive time-varying delays. By applying matrix inequality technique and exploiting reciprocally convex approach, several delay-dependent criteria are presented in the form of linear matrix inequalities (LMIs) to ensure the global synchronization of CVNNs via structuring an appropriate Lyapunov–Krasovskii functional. An example with simulations is provided to ensure the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

This paper investigates the L 2 – L ∞ state estimation problem for a class of delayed neural networks. Attention is focused on the design of a full-order state estimator such that the prescribed L 2 – L ∞ performance constraint can be ensured. By utilizing the time-delay information sufficiently, a novel L 2 – L ∞ performance analysis approach is proposed in this paper for the first time. Based on such an approach, the less conservative sufficient conditions are established in terms of linear matrix inequalities under which the L 2 – L ∞ performance level can be achieved for the estimation error dynamics. Several numerical examples show that the proposed approach in this paper is explicitly effective in reducing the possible conservatism. [ABSTRACT FROM AUTHOR]

This paper investigates the H ∞ and l 2 − l ∞ filtering problem for discrete stochastic nonlinear system with randomly occurring gain variations and quantization effects over a finite horizon. The system under consideration is subject to time-varying parameters and exogenous signals. A Bernoulli distributed white sequence with a known conditional probability is introduced to describe the binary switching phenomenon between two types of nonlinear disturbances. The randomly occurring filter gain variations are utilized to express the random change of filter parameters that is governed by a binary sequences taking values on 0 or 1. Moreover, the quantization effects of measurements are also taken into account where a form of logarithmic quantizer is applied. By using the recursive linear matrix inequalities (RLMIs) approach, sufficient conditions are established for the existence of the desired finite-horizon filter to guarantee the H ∞ and l 2 − l ∞ performance specifications at the same time. A numerical example is proposed to show the correctness and effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative. [ABSTRACT FROM AUTHOR]

This paper investigates the passivity analysis problem for a class of discrete-time neural networks subject to the mixed time-delays and randomly occurring quantization effects. Both the time-varying discrete delays and the infinite distributed time-delays are considered. The phenomenon of randomly occurring logarithmic quantization is taken into consideration, which is described by a random sequence obeying the Bernoulli distribution. Sufficient conditions are established, guaranteeing the globally asymptotical stability in the mean square and the strict ( Q , S , R ) − γ -dissipative property of the considered neural networks. The main results are proposed by virtue of the linear matrix inequality approach that can be easily solved by certain convex optimization algorithms. The obtained methodology is capable of being adopted in the passivity analysis with little modifications. A numerical example is provided to verify the correctness and effectiveness of the exploited methodology. [ABSTRACT FROM AUTHOR]

The stability of fractional-order complex-valued neural networks (FOCVNNs) with probabilistic time-varying delays is investigated in this paper. By constructing suitable Lyapunov–Krasovskii functional and utilizing inequality technique, a complex-valued linear matrix inequality (LMI) criterion guaranteeing the global asymptotic stability of the proposed FOCVNNs is deduced. A numerical example with simulations is provided to demonstrate the feasibility and availability of the obtained theoretical result. [ABSTRACT FROM AUTHOR]

The problem on passive filter design for fractional-order quaternion-valued neural networks (FOQVNNs) with neutral delays and external disturbance is considered in this paper. Without separating the FOQVNNs into two complex-valued neural networks (CVNNs) or the FOQVNNs into four real-valued neural networks (RVNNs), by constructing Lyapunov–Krasovskii functional and using inequality technique, the delay-independent and delay-dependent sufficient conditions presented as linear matrix inequality (LMI) to confirm the augmented filtering dynamic system to be stable and passive with an expected dissipation are derived. One numerical example with simulations is furnished to pledge the feasibility for the obtained theory results. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust stability analysis of fractional-order quaternion-valued neural networks (FOQVNNs) with neutral delay and parameter uncertainties. Without transforming the FOQVNNs into equivalent two complex-valued systems or four real-valued systems, based on homeomorphism principle, matrix inequality technique and Lyapunov method, both delay-independent and delay-dependent criteria to guarantee the existence, uniqueness and global stability of equilibrium point for the considered FOQVNNs are derived in the form of linear matrix inequality (LMI). Two examples with simulations are provided to manifest the theoretical results. [ABSTRACT FROM AUTHOR]

Stability problem of quaternion-valued neutral-type delayed neural networks (QVNTDNNs) is researched in this paper. By utilizing homeomorphism principle, matrix inequality technique and Lyapunov method, both delay-independent and delay-dependent stability criteria are established in the form of linear matrix inequalities to pledge the existence, uniqueness and global stability of the equilibrium point of the considered QVNTDNNs. An example with simulations is given to manifest the validity of the exported results. [ABSTRACT FROM AUTHOR]

In this paper, the robust stability of uncertain fractional order singular systems with neutral and time-varying delays is investigated. By applying Lyapunov–Krasovskii functional approach, several sufficient conditions in the form of linear matrix inequality to ensure asymptotical stability and robust stability are derived for the considered systems. The advantage of the employed method in this paper is that one may directly calculate integer-order derivatives of Lyapunov–Krasovskii functional. Several simple examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotical synchronization of two nonidentical complex-valued neural networks (CVNNs) with leakage delay and time-varying delays via integral sliding mode control approach. A suitable sliding surface and an appropriate Lyapunov–Krasovskii functional are constructed. By using free-weighting matrix method combined with inequality technique, a sliding mode controller is designed to ensure the synchronization for the considered CVNNs. The obtained criterion is presented in the form of complex-valued linear matrix inequalities (LMIs), which could be calculated through YALMIP with solver of SDPT3 in MATLAB. An example is provided to demonstrate the obtained theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, the problem of global µ -stability for quaternion-valued neural networks with time-varying delays and unbounded distributed delays is investigated. To avoid the non-commutativity of quaternion multiplication, the quaternion-valued neural networks is decomposed into two complex-valued systems. By employing the homomorphic mapping principle, a sufficient condition for the existence and uniqueness of equilibrium point of the considered quaternion-valued neural networks is proposed in the form of linear matrix inequality (LMI) in complex-valued domain. Further, the appropriate Lyapunov–Krasovkii functional is constructed in the Hermitian quadratic form, and sufficient condition to ensure the global µ -stability of the equilibrium point is obtained by using inequality technique. Finally, two numerical examples with simulations are provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the l 2 − l ∞ state estimation problem for discrete-time switched neural networks with time-varying delay. The main objective is to design a mode-dependent state estimator such that the error dynamics is exponentially stable with a weighted l 2 − l ∞ performance level. By incorporating the novel l 2 − l ∞ performance analysis approach, the augmented piecewise Lyapunov-like functionals, the discrete Wirtinger-based inequality and the average-dwell-time switching, less conservative sufficient conditions are proposed by means of linear matrix inequalities. A numerical example is given to illustrate the effectiveness and benefits of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed state estimation problem for a class of time-varying systems over sensor networks. An event-triggered communication scheme is utilized to save the constrained computation resource and network bandwidth while preserving the desired performance. The measurements on each node are transmitted to the estimators only when a certain triggering condition is satisfied. Moreover, in order to improve the reliability of data transmission services, we exploit redundant communication channels during the transmission process. The purpose of this paper is to design a set of time-varying state estimators such that the dynamics of the state estimation error satisfies the average H ∞ performance constraints. The specific gains of the estimator can be obtained by calculating a series of recursive linear matrix inequalities (RLMIs). Finally, a simulation example is presented to show the effectiveness of the state estimation method proposed in this paper. [ABSTRACT FROM AUTHOR]

The data missing is a common and important problem in the area of genetic regulatory networks (GRNs). A class of discrete-time GRNs with missing values, parameter uncertainties, time delays and molecular noise is considered in this paper. A set-membership filtering method is proposed to estimate the states of the underlying GRNs. Meanwhile, the corresponding problem of set-membership filtering is formulated as finding the set of estimations that belongs to an ellipsoid. The desired filter gains are characterized as the solution of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method, which shows that by using the proposed set-membership filtering algorithm, the concentrations of mRNA and protein could be estimated accurately. [ABSTRACT FROM AUTHOR]

In this note, the probability-guaranteed set-membership filtering problem is investigated for a class of time-varying systems with incomplete measurements. The uniform distribution over known finite ranges is assumed for mutually independent stochastic variables existing in the functions of system matrices. The process noise and measurement noise are unknown, bounded and confined to a specified ellipsoidal set respectively, which is handled by transformation to the inequality constraints. The purpose is to design a set-membership filter, for all the admissible unknown but bounded noises, known deterministic input and incomplete measurements, such that the ellipsoidal set including all possible states can be determined by a convex optimization approach with probability constraint. A recursive linear matrix inequality (RLMI) approach is proposed to address the probability-guaranteed set-membership filtering problem. Finally, a simulation example demonstrates the effectiveness of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]