Passivity Criteria Research Articles

LMI-Based Results on Robust Exponential Passivity of Uncertain Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays via the Reciprocally Convex Combination Technique

The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, the lower bounds of the delays are allowed to be either positive or zero adopting the combination of the model transformation, various inequalities, the reciprocally convex combination, and suitable Lyapunov–Krasovskii functional. A new robust exponential passivity criterion is received and formulated in the form of linear matrix inequalities (LMIs). Moreover, a new exponential passivity criterion is also examined for systems without uncertainty. Four numerical examples indicate our potential results exceed the previous results.

New delay and order-dependent passivity criteria for impulsive fractional-order neural networks with switching parameters and proportional delays

This work deals with the problem of passivity analysis of fractional-order neural networks (FONNs) with impulse, proportional delays and state-dependent switching parameters. The novelty of the work lies in addressing the crucial issue of developing a delay-dependent LMI condition for analysing the behaviour of delayed FONNs. In this paper, a new lemma on Caputo fractional derivatives is developed to construct a new Lyapunov functional to derive delay dependent LMI condition for the passivity analysis of FONNs. Besides that, under modification, another sufficient condition is derived to give an impulse gain-dependent LMI condition. Moreover, for the first time in the literature, delay-dependent and order-dependent passivity criteria for fractional-order systems with proportional delays are presented in this paper. Finally, the results obtained are verified with suitable numerical parameter values and the simulation results are demonstrated to show the effectiveness of the proposed method and superiority of FONNs.

Passivity-Based Fuzzy ISMC for Wind Energy Conversion Systems With PMSG

This paper investigates the fuzzy integral sliding-mode control (ISMC) for permanent magnet synchronous generator (PMSG)-based wind energy conversion systems (WECSs). To do this, by using the double orthogonal complement and Frobenius theorem, the existence condition of the fuzzy sliding surface is presented. By constructing a suitable fuzzy Lyapunov function and introducing slack matrices, the sufficient conditions are gained via linear matrix inequalities (LMIs) for the concerned model to be asymptotically stable and passive. Further, the reachability of the switching surface is ensured by the considered fuzzy sliding-mode control laws. Besides that an adaptive fuzzy ISMC is constructed to derive the passivity criterion. For the demonstration, the presented control strategy is validated with nonlinear PMSG-based WECS. Finally, the effectiveness of the derived theoretical result is established by the numerical parameter values of PMSG-based wind-turbine model.

STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology.

Design of Stochastic Passivity and Passification for Delayed BAM Neural Networks with Markov Jump Parameters via Non-uniform Sampled-Data Control

This paper investigates the issue of passivity and passification for delayed Markov jump bidirectional associate memory (BAM)-Type neural networks via non-uniform sampled-data control. By utilizing the Lyapunov–Krasovskii functional strategy, a novel delay-dependent passivity criterion is developed with respect to linear matrix inequalities to guarantee the Markov jump delayed BAM neural frameworks to be passive. At that point, in view of the got passivity conditions, the passification issue is further tackled by planning a mode-dependent non-uniform sampled-data controller design is presented. Finally, a numerical example is provided to illustrate the applicability and effectiveness of the theoretical result.

Robust Finite Time Passivity and Stabilization of Uncertain Switched Nonlinear System

This paper studies the robust finite time passivity, feedback robust finite time passification and global finite time stabilisation of the switched nonlinear systems with structural uncertainties. First, a concept of robust finite time passivity is proposed. Each subsystem is not required to be robust finite time passive. Namely, each active subsystem is finite time passive, even if there exists uncertainties in the switched system. Based on this finite time passivity concept, the finite time stability is obtained for switched nonlinear systems. Second, the robust finite time passivity criterion of switched system is established by the design of a state-dependent switching law. Third, a state-dependent switching law and a set of state feedback controllers are designed to render the closed loop system finite time passive. Finally, the robust finite time passivity property is preserved for the feedback interconnected uncertain switched systems. A numerical example is given to verify the effectiveness of our results.

PD and PI Control for Passivity and Synchronization of Coupled Neural Networks With Multi-Weights

This paper mainly discusses the passivity and synchronization for a coupled neural networks with multi-weights (CNNMWs) by virtue of devised proportional-integral-derivative (PID) controllers. On one side, several passivity criteria for the CNNMWs are put forward on the basis of suitable Lyapunov functional, inequality techniques and devised proportional-derivative (PD) controller, and the output-strict passivity is employed to cope with the synchronization of the CNNMWs. On the other side, we also investigate the passivity of the CNNMWs by choosing appropriate proportional-integral (PI) controller, and a criterion of synchronization is developed for the CNNMWs. Lastly, the obtained criteria of passivity and synchronization are verified by adopting two numerical examples.

Passivity and Dissipativity of Fractional-Order Quaternion-Valued Fuzzy Memristive Neural Networks: Nonlinear Scalarization Approach.

In this article, the problem of passivity and dissipativity analysis is investigated for a class of fractional-order quaternion-valued fuzzy memristive neural networks. Based on the famous nonlinear scalarizing function, a nonlinear scalarization method is developed, which can be employed to compare the "size" of two different quaternions. In this way, the convex closure proposed by the quaternion-valued connection weights is meaningful. By constructing proper Lyapunov functional, several improved passivity criteria and dissipativity conclusions are established, which can be checked efficiently by utilizing some standard mathematical calculations. Finally, the obtained results are validated by simulation examples.

Passivity-Based Robust Sampled-Data Control for Markovian Jump Systems

In this paper, the problem of passivity-based robust sampled-data control is investigated for continuous-time Markovian jump systems (MJSs). First, using parameters-dependent Lyapunov functionals consisting of looped-functionals, stochastic sufficient passivity criteria for continuous-time polytopic uncertain MJSs are proposed. As a corollary, we get the stochastic sufficient passivity criteria for continuous-time nominal MJSs. Based on the obtained stochastic sufficient passivity criteria, time-independent state feedback sampled-data controllers are designed. Then, in order to get a time-dependent state feedback sampled-data controller, parameters-dependent time-scheduled Lyapunov functionals consisting of looped-functionals are developed. New stochastic sufficient passivity criteria are obtained. Furthermore, based on the stochastic sufficient passivity criteria, the time-dependent state feedback sampled-data controllers are designed. Four numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Event-triggered passivity of multi-weighted coupled delayed reaction-diffusion memristive neural networks with fixed and switching topologies

This paper solves the event-triggered passivity problem for multiple-weighted coupled delayed reaction-diffusion memristive neural networks (MWCDRDMNNs) with fixed and switching topologies. On the one side, by designing appropriate event-triggered controllers, several passivity criteria for MWCDRDMNNs with fixed topology are derived based on the Lyapunov functional method and some inequality techniques. Moreover, some adequate conditions for ensuring asymptotical stability of the event-triggered passive network are presented. On the other side, we take the switching topology in network model into consideration, and investigate the event-triggered passivity and passivity-based synchronization for MWCDRDMNNs with switching topology. Finally, two examples with numerical simulation results are provided to illustrate the effectiveness of the obtained theoretical results.

Passivity Analysis of Non-autonomous Discrete-Time Inertial Neural Networks with Time-Varying Delays

This paper addresses the passivity problem for delayed non-autonomous discrete-time inertial neural networks (NDINN), including the discrete-time switched inertial neural networks (DSINN) with state-dependent discontinuous right-hand side as its special case. First, we take a linear transformation to transform the original network into first-order difference equations. Second, by utilizing the Lyapunov direct method and with the help of the property of maximum singular value, we present a passivity criterion for the NDINN with delay-dependent linear matrix inequalities. Combining with the characteristic function method, the proposed analytical approach for NDINN is further extended to the DSINN. Finally, two simulation examples validate the efficacy of the analytical results.

Characterization of passivity in Mueller matrices.

Except for very particular and artificial experimental configurations, linear transformations of the state of polarization of an electromagnetic wave result in a reduction of the intensity of the exiting wave with respect to the incoming one. This natural passive behavior imposes certain mathematical restrictions on the Mueller matrices associated with the said transformations. Although the general conditions for passivity in Mueller matrices were presented in a previous paper [ J. Opt. Soc. Am. A17, 328 (2000)JOAOD60740-323210.1364/JOSAA.17.000328], the demonstration was incomplete. In this paper, the set of two necessary and sufficient conditions for a Mueller matrix to represent a passive medium are determined and demonstrated on the basis of its arbitrary decomposition as a convex combination of nondepolarizing and passive pure Mueller matrices. The procedure followed to solve the problem also provides an appropriate framework to identify the Mueller matrix that, among the family of proportional passive Mueller matrices, exhibits the maximal physically achievable intensity transmittance. Beyond the theoretical interest on the rigorous characterization of passivity, the results obtained, when applied to absolute Mueller polarimetry, also provide a criterion to discard those experimentally measured Mueller matrices that do not satisfy the passivity criterion.

Arbitrary decomposition of a Mueller matrix.

Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie the analysis and interpretation of the measured Mueller matrices and, very particularly, on the theorems for their serial and parallel decompositions. In this Letter, the most general formulation for the parallel decomposition of a Mueller matrix is presented, which overcomes certain critical limitations of the previous approaches, particularly the unnecessary exigency that the Mueller matrices of all parallel components have to be normalized in order to have equal transmittances for unpolarized light. In addition, the obtained results lead to a generalization of the polarimetric subtraction procedure and allow for a formulation of the arbitrary decomposition that integrates, in a natural way, the passivity criterion.

Passivity and passification of quaternion‐valued memristive neural networks

In this paper, a class of memristive neural networks with quaternion‐valued connection weights is studied. By starting from some basic quaternion‐valued algorithms, the quaternion‐valued memristive system is obtained; then, some passivity criteria for the memristive neural networks are presented based on some appropriate auxiliary functions. Furthermore, to tackle with the passification problem, two kinds of control protocols are designed. What should be mentioned is that, in the above derived conclusions, the partial order is employed, which can be employed to compare the “magnitude” of two different quaternions, and thus, the closed convex hull consisted by quaternion can be derived correspondingly. In the end, the analytical design are substantiated with two numerical results.

Pinning control for passivity and synchronization of coupled memristive reaction–diffusion neural networks with time-varying delay

This paper studies the passivity and synchronization problems of delayed coupled memristive reaction–diffusion neural networks (CMRDNNs) by utilizing two pinning control schemes, respectively. Firstly, a nodes-based controller is added to the delayed coupled memristive reaction–diffusion neural network model, and some sufficient conditions are derived to ensure the passivity and synchronization of the presented network through constructing appropriate Lyapunov functionals. Additionally, with the help of an edges-based pinning adaptive strategy and inequality techniques, several passivity criteria are further established. Moreover, a similar pinning control method is employed in order to guarantee the synchronization of delayed CMRDNNs. Eventually, two examples are provided to confirm the validity of the obtained results.

Multivariable High-Frequency Input-Admittance of Grid-Connected Converters: Modeling, Validation, and Implications on Stability

Modern grids are facing a massive integration of power electronics devices, usually associated to instability issues. In order to assess the likelihood and severity of harmonic instability in the high-frequency region, this paper develops a multivariable input-admittance model that accurately reflects the following aspects: 1) the discrete controller frequencies are defined inside a spectrum region limited by the Nyquist frequency and 2) the physical system aliases are transformed into lower frequency component inside the discrete controller. The proposed model shows that dynamic interactions are not theoretically band-limited; however, the control action tends to be strongly limited in a low-frequency range, due to the natural low-pass filter behavior of acquisition and modulation blocks. This is reflected in a reduced resistive part (either positive or negative) of the input-admittance in the high-frequency range. More specifically, considering the input-admittance passivity criterion, the excursions into the nonpassive area are very smooth at high frequencies, where the input-admittance is well-described by simply its inductive filter. Comprehensive experiments are conducted on a lab scale prototype, which includes measurements beyond the Nyquist frequency and alias identification. The experimental results well-match the theoretical model.

Passivity and passification of memristive neural networks with leakage term and time-varying delays

This paper investigates passivity and passification for memristive neural networks (MNNs) with both leakage and time-varying delays. MNNs are converted into traditional neural networks (NNs) by nonsmooth analysis, then sufficient conditions are derived to guarantee the passivity based on Lyapunov method. A novel Lyapunov–Krasovskii functional (LKF) is constructed without requiring all the symmetric matrices to be positive definite. The relaxed passivity criteria with less conservativeness or complexity are obtained in the form of linear matrix inequalities (LMIs), which can be verified easily by the LMI toolbox. Then, the passification controller is designed with the relaxed criteria to ensure that MNNs with both leakage and time-varying delays are passive. Finally, two pertinent examples are presented to show the effectiveness of the theoretical results.

Impulsive control for passivity and exponential synchronization of coupled neural networks with multiple weights

This paper investigates the passivity and synchronization problems for two classes of multiple weighted coupled neural networks (MWCNNs) with or without time delays. Firstly, by utilizing an impulsive control strategy and some inequality techniques, several passivity criteria for MWCNNs with diverse dimensions of output and input are established. Then, based on the Lyapunov functional, some sufficient conditions to ensure the synchronization of MWCNNs via impulsive control are derived. In addition, combined with the comparison principle and the impulsive delay differential inequality, the global exponential synchronization of MWCNNs with time-varying delays is considered under impulsive control. Finally, two numerical examples illustrate the effectiveness of the obtained results.

Passivity Analysis for Quaternion-Valued Memristor-Based Neural Networks With Time-Varying Delay.

This paper is concerned with the problem of global exponential passivity for quaternion-valued memristor-based neural networks (QVMNNs) with time-varying delay. The QVMNNs can be seen as a switched system due to the memristor parameters are switching according to the states of the network. This is the first time that the global exponential passivity of QVMNNs with time-varying delay is investigated. By means of a nondecomposition method and structuring novel Lyapunov functional in form of quaternion self-conjugate matrices, the delay-dependent passivity criteria are derived in the forms of quaternion-valued linear matrix inequalities (LMIs) as well as complex-valued LMIs. Furthermore, the asymptotical stability criteria can be obtained from the proposed passivity criteria. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

Passivity and Passification of Dynamic Memristor Neural Networks with Delays Operating in the Flux-Charge Domain

In this paper, the passivity and passification issue are considered for a class of dynamic memristor neural networks (DMNNs) with delays. Different from the models with respect to memristive neural networks in the literature, the flux-controlled dynamic memristors are used in the neurons and finite concentrated delays are accounted for in the interconnections. With the construction of suitable Lyapunov-Krasovskii functional (LKF), a novel passivity criteria, which involves the interconnection matrix, the delayed interconnection matrix and nonlinear memristor, is addressed in the form of linear matrix inequalities (LMIs) in the flux-charge domain. In addition, for state feedback passification, two procedures for designing passification controllers are proposed in terms of LMIs to guarantee that the considered DMNNs are passive. Finally, two examples are provided to illustrate the validity of the theoretical results.