Mode-dependent Delays Research Articles

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.

Stability of nonlinear positive semi-Markovian jump systems with mode-dependent delay subject to mode-dependent average dwell time

This article concentrates on the stability of nonlinear positive semi-Markovian jump systems (NPSMJSs) with mode-dependent delay, where the transition rate functions depend on both the sojourn-times and the average dwell time (ADT) switching. By resorting to linear programming (LP) approach, sufficient conditions for stochastic exponential stability of mode-dependent delay for NPSMJSs are developed. In addition, we obtain the $ L_{1}- $gian performance analysis. Finally, two numerical examples are proposed to illustrate the advantages of the theoretical results.

Stability analysis of semi-Markov switching stochastic mode-dependent delay systems with unstable subsystems

This paper is dedicated to studying the stability of semi-Markov switching stochastic delay systems with unstable subsystems, where delay depends on another semi-Markovian process and transition rates are uncertain. Based on the stochastic analysis theory and the mode-dependent multi-Lyapunov function method, relevant sufficient conditions are established to ensure the asymptotic stability in mean square of the system. In addition, contrary to the existing works, the system under consider is more general and our works are not only applicable to the system with partial unstable subsystems, but also applicable to the system with all unstable subsystems. Finally, one numerical example is provided to illustrate the correctness of the method described in the paper.

Event-Triggered Synchronization of Multiple Discrete-Time Markovian Jump Memristor- Based Neural Networks With Mixed Mode-Dependent Delays

This paper deals with global synchronization problem of multiple discrete-time Markovian jump memristor-based neural networks (DTMJMNNs) with mixed mode-dependent delays via a novel event-triggered impulsive coupling control (ETICC). The parameters of the multiple DTMJMNNs and the mixed time delays (both discrete and distributed delays) switch randomly according to a Markov chain. In the ETICC strategy, the controller does not work all the time, but only works at impulse instants determined by specific events. In particular, the coupling matrix can be non-Laplacian. By using the Lyapunov stability theory, linear matrix inequalities (LMIs), and the Kronecker product, some sufficient conditions for global synchronization of multiple DTMJMNNs under the event-triggered strategy are derived. Two examples are presented to test the validity of the theoretical analysis results.

Mode-dependent delays for dissipative filtering of stochastic semi-Markovian jump for neural networks

This work is concerned with the issue of dissipative filtering for stochastic semi-Markovian jump via neural networks where the time-varying delay is based upon another semi-Markov process. Dissipative performance analysis is employed to solve a mode-dependent filtering problem in a unified way. To achieve this task, we implemented the recently proposed notion of extended dissipativity, which gives an inequality equivalent to the well-known H_{infty }, L_{2}–L_{infty }, and dissipative performances. Different from the existing literature (Arslan et al. in Neural Netw 91:11–21, 2017; Chen et al. in ISA Trans. 101:170–176, 2020) where mostly delay-free filters have been investigated, our filter contains a communication delay. Based upon the delay-dependent conditions, for the analysis of stochastic stability and extended dissipativity for neural networks with time-varying delays, our results are obtained by using a mode-dependent Lyapunov–Krasovskii functional together with a novel integral inequality. Original stochastic filtering conditions are characterized by linear matrix inequalities. A numerical simulation is elaborated to elucidate the feasibility of the proposed design methodology.

Finite-time filtering of T-S fuzzy semi-Markov jump systems with asynchronous mode-dependent delays

This paper studies the finite-time filter design of semi-Markov jump system by Takagi-Sugeno (T-S) fuzzy rules. Asynchronous mode-dependent delays are concerned to describe more practical random features, which implies that the semi-Markov process of system state is different from another semi-Markov process of mode-dependent time-varying delays. With the help of model transformation as well as mode-dependent Lyapunov-Krasovskii function method, sufficient criteria are first established for maintaining finite-time passivity performance of filtering errors. Then, the matrix technique is employed to synthesize the filter gain design. In the end, the applicableness and effectiveness of our developed results are confirmed by an illustrative example.

Demonstration of QPSK data correlation and equalization using a tunable optical tapped delay line based on orbital angular momentum mode delays

We demonstrate a tunable optical tapped delay line (OTDL) using delays based on orbital angular momentum (OAM) modes to perform data correlation and equalization for a quadrature phase-shift-keyed (QPSK) signal. The system: (i) creates N signal replicas as N taps on different OAM modes through mode multicasting, (ii) tunes the complex tap weights (i.e., amplitude and phase of the modes), (iii) applies a tunable mode-dependent delay to each replica, and (iv) coherently combines the taps in order to realize the OTDL functions of correlation and equalization. The experiment results: (i) identify the correlation occurrence of a sequence of 2 or 3 symbols in an incoming 10 or 20 Gbaud QPSK signal, and (ii) equalize the distortion caused by chromatic dispersion for a 20-Gbaud QPSK data signal and reduce error vector magnitude (EVM) from ∼25.4 to ∼12.9%.

Formula omitted] estimation for stochastic semi-Markovian switching CVNNs with missing measurements and mode-dependent delays

This article is devoted to the H∞ estimation problem for stochastic semi-Markovian switching complex-valued neural networks subject to incomplete measurement outputs, where the time-varying delay also depends on another semi-Markov process. A sequence of random variables with known statistical property is introduced to depict the missing measurement phenomenon. Based on the generalized Itoˆ’s formula in complex form concerning with the semi-Markovian systems, complex-valued reciprocal convex inequality as well as intensive stochastic analysis method, some mode-dependent sufficient conditions are presented guaranteeing the estimation error system to be exponentially mean-square stable with a prespecified H∞ disturbance attenuation level. In addition, the mode-dependent estimator gain matrices are appropriately designed according to the feasible solutions of certain complex matrix inequalities. In the end, one numerical example is provided to illustrate effectiveness of the theoretical results.

Reliable dissipative control for fuzzy singular semi-markovian jump systems with mode-dependent delays and randomly occuring uncertainties

This article addresses the problem of dissipative control for fuzzy singular semi-Markovian jump systems with actuator faults, mode-dependent delays and randomly occuring uncertainties. Firstly, Takagi-Sugeno fuzzy model is utilized to describe the singular nonlinear semi-Markovian jump delayed systems. Then, a more general actuator fault model is considered and the fuzzy reliable controller is designed. Based on the delay system method, dissipative control theory and linear matrix inequality techniques, multiple appropriate Lyapunov-Krasovskii functional candidates are constructed to propose sufficient conditions which guarantee that fuzzy singular semi-Markovian jump delayed system is stochastically admissible and strictly (W,Y,S)−α dissipative. Finally, two simulation examples including the DC motor driving model are presented to affirm the effectiveness of the obtained results.

Stability of nonlinear stochastic Markov jump system with mode-dependent delays and applications

ABSTRACT The pth moment stability of stochastic Markov jump systems (SMJSs) with time-delays and polynomial growth was investigated in this paper. Both the involved time-delays and polynomial growth are mode dependent. By using the new property of the polynomial as well as the relation between the time-delay and the generator of the Markov-chain, sufficient pth moment stability criteria are proposed. Meanwhile, the robustness of the stable SMJSs is also considered, which reveals that how much perturbation the stable SMJSs can tolerate. As an application, the consensus of stochastic multi-agent systems with nonlinear dynamics is investigated. Finally, the effectiveness of our results is illustrated by examples.

Event-triggered state estimation for Markovian jumping neural networks: On mode-dependent delays and uncertain transition probabilities

This paper is concerned with the event-triggered state estimation (ETSE) problem for a class of discrete-time Markovian jumping neural networks with mode-dependent time-delays and uncertain transition probabilities. The parameters of the neural networks experience switches that are characterized by a Markovian chain whose transition probabilities are allowed to be uncertain. The event-triggered mechanism is introduced in the sensor-to-estimator channel to reduce the frequency of signal communication. The aim of this paper is to develop an ETSE scheme such that the estimation error dynamics is exponentially ultimately bounded in the mean square. To achieve the aim, two sufficient conditions are proposed with the first one guaranteeing the existence of the required state estimator, and the second one giving the algorithm for designing the corresponding estimator gain by solving some matrix inequalities. In the end, the validity of the proposed estimation scheme is illustrated by a numerical example.

H ∞ consensus of multi-agent systems with semi-Markovian switching topologies and mode-dependent delays

This paper addresses leader-following consensus of multi-agent systems with semi-Markovian switching topologies and time-varying delays. Unlike the classic Markovian switching topologies, the transition rates are time-varying in the semi-Markovian switching topologies, which can better model the switching of topologies due to inevitable stochastic changes. Moreover, compared with existing works on multi-agent systems with switching topologies and time delays, the delays in the paper are dependent on the switching modes. By designing the distributed mode-dependent consensus protocol and constructing Lyapunov functional, sufficient conditions in terms of LMIs are derived to ensure that leader-following consensus is asymptotically achieved in the mean square. Finally, a numerical example is provided to show the effectiveness of the main results.

Stabilization of piecewise-homogeneous Markovian switching CVNNs with mode-dependent delays and incomplete transition rates

This paper is devoted to the problems of exponential stability and stabilization for piecewise-homogeneous Markovian switching complex-valued neural networks with incomplete transition rates (TRs). Both the time-varying delays and the coefficient matrices are switched among finite modes governed by a piecewise-homogeneous Markov process, where the TRs of the two-level Markov processes are assumed to be time-varying during different intervals. On the basis of an appropriately chosen Lyapunov–Krasovskii functional, some mode-dependent sufficient conditions are presented to guarantee the unforced network to be exponentially mean-square stable. Then, by proposing certain mode-dependent state feedback controller, stabilization criteria are derived through strict mathematical proofs. At the end of the paper, numerical examples are provided to illustrate the effectiveness of the theoretical results.

Wavelength Demultiplexer Designs Operating Over Multiple Spatial Modes of a Rectangular Waveguide

Wavelength demultiplexers are instrumental in wavelength division multiplexing (WDM) communications. In advance of space-division multiplexing (SDM) WDM communications, we investigate wavelength multiplexer/demultiplexer designs operating over multiplexed spatial modes simultaneously, when the modes are arranged along one transverse direction of a rectangular waveguide. The demultiplexer waveguides’ modes match those of rectangular core fibers, enabling simple and efficient edge-coupling. We describe the challenge of demultiplexing mode division multiplexed (MDM) channels, and suggest guided optics solutions for its implementation. We analyze the spatial–spectral interplay at output waveguide coupling due to mode dependent phase delays in arrayed waveguide grating router demultiplexer design, and offer low mode dependent loss solutions. The proposed schemes allow for efficient and compact MDM-enabled WDM multiplexing, paving the way to SDM-WDM communication networks.

Complex lattice reduction aided detection for mode-division multiplexing systems with mode dependent loss and differential mode group delay

The performance of mode-division multiplexing (MDM) system is normally limited to mode dependent loss (MDL) and differential mode group delay (DMGD). Where MDL seriously deteriorates the orthogonality of the transmission matrix, resulting the traditional equalization algorithm failure. DMGD causes large dimension of transmission matrix in time domain, leading to equalization difficulties. In this work, we propose a linear detector method based on complex lattice reduction (CLR) algorithm for MDM orthogonal frequency-division multiplexing (OFDM) system with MDL and DMGD. CLR algorithm as an effective mathematical tool which can improve the orthogonality of the transmission matrix. The OFDM modulation solves the problem of large transmission matrix dimension caused by DMGD. The proposed method nearly reaches the performance of maximum likelihood (ML) but with lower computational complexity. The simulation result shows that the optical signal to noise ratio (OSNR ) penalty of the proposed algorithm is 3dB lower than that of zero-forcing (ZF) and minimum mean square error (MMSE) equalizers at a transmission distance of 1200 km with Goffset is 2dB.

Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays

This paper is concerned with the problem of non-fragile delay feedback control for neutral stochastic Markovian jump systems (NSMJSs) with time-varying delays. The main aim is to design non-fragile and mode-dependent delay feedback controller (DFC) both in the drift part and in the diffusion part to realize closed-loop NSMJS is stochastically stable. By constructing mode-dependent and delay-dependent comprehensive Lyapunov-Krasovskii functional, the stabilization conditions are provided in terms of linear matrix inequalities (LMIs). Simulation examples including a lossless transmission line model (LTLM) are utilized to verify the validity and usefulness of the proposed method.

Fault detection filter design for continuous-time nonlinear Markovian jump systems with mode-dependent delay and time-varying transition probabilities

This paper focuses on fault detection filter (FDF) design for continuous-time nonlinear Markovian jump systems (NMJSs) with mode-dependent delay and time-varying transition probabilities (TPs). By using a novel Lyapunov-Krasovskii function and based on convex polyhedron technique, a new FDF, as the residual generator, is constructed to guarantee the mean-square exponential stability and a prescribed level of disturbance attenuation for admissible perturbations of NMJSs. Finally, the numerical simulation is carried out to demonstrate the effectiveness of our method.

LOCAL SYNCHRONIZATION OF MARKOVIAN NEURAL NETWORKS WITH NONLINEAR COUPLING

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

Reliable filter synthesis for a class of stochastic systems under nonhomogeneous Markovian switching

This paper is concerned with the problem of reliable filter synthesis for a class of stochastic systems with random occurring nonlinearities and mode-dependent delays under nonhomogeneous Markovian switching. By considering a new sensor failure model, which is valid to describe the drift faults, the loss of effectiveness, the stuck as well as the outage faults besides the normal case, a procedure of filter synthesis is proposed. Further, the filter gains are characterized in terms of solutions to a convex optimization problem with less conservativeness. Finally, the theoretical results are illustrated through an example of the aircraft engine.

Global synchronization of discrete-time coupled neural networks with Markovian switching and impulses

This paper is concerned with the problem of synchronization analysis for discrete-time coupled neural networks. The networks under consideration are subject to: (1) the jumping parameters that are modeled as a continuous-time, discrete-state Markov process; (2) impulsive disturbances; and (3) time delays that include both the mode-dependent discrete and distributed delay. By constructing suitable Lyapunov–Krasovskii functional and combining with linear matrix inequality approach, several novel criteria are derived for verifying the global exponential synchronization in the mean square of such stochastic dynamical networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. A simulation example is presented to show the effectiveness and applicability of the obtained results.