Passivity Criteria Research Articles

Stability and passivity analysis of delayed neural networks via an improved matrix-valued polynomial inequality

The stability and passivity of delayed neural networks are addressed in this paper. A novel Lyapunov–Krasovskii functional (LKF) without multiple integrals is constructed. By using an improved matrix-valued polynomial inequality (MVPI), the previous constraint involving skew-symmetric matrices within the MVPI is removed. Then, the stability and passivity criteria for delayed neural networks that are less conservative than the existing ones are proposed. Finally, three examples are employed to demonstrate the meliority and feasibility of the obtained results.

Passivity analysis of neutral‐type Cohen–Grossberg neural networks involving three kinds of time‐varying delays

This paper discusses the issue of passivity analysis of the neutral‐type Cohen–Grossberg neural networks (NTCGNNs) with distributed, transmission, and neutral time‐varying delays. A new method based on the system solutions was proposed to analyze passivity. It is important to note that this paper focuses solely on introducing the proposed method and does not provide a comprehensive analysis of NTCGNNs. This method does not require for the construction of Lyapunov–Krasovskii functional (LKF) or model transformation, thus reducing computational effort and complexity. By using this new way and the inequality technique, a passivity criterion for NTCGNNs with multiple time‐varying delays is derived. The applicability of the derived criterion was demonstrated through a numerical example.

Improved Robust Passivity Criteria for Delayed Neural Networks

Improved Robust Passivity Criteria for Delayed Neural Networks

Passivity and robust passivity of impulsive inertial neural networks with proportional delays under the non-reduced order approach

This paper primarily addresses the problems of passivity and robust passivity of impulsive inertial neural networks (IINNs) with proportional delays. By constructing the Lyapunov functional directly on the original system using the non-reduced order approach, some passivity and robust passivity criteria for IINNs are addressed. In comparison with the order reduction method utilized in the existing articles, the non-reduced order method is more in line with real requirements and can better analyze the dynamic behavior of inertial neural networks (INNs). Meanwhile, the results in this paper are all in algebraic form, which are easy to verify. To demonstrate the effectiveness of the results derived, numerical examples are presented at the end.

Delay-dependent passivity of impulsive coupled reaction–diffusion neural networks with multi-proportional delays

This article deals with passivity of coupled reaction–diffusion neural networks (CRDNNs) with multi-proportional delays and impulses. Two aspects are mainly considered: one is that the coupling term of the system depends on the delay, and the other is that the coupling term of the system is delay-independent. In order to simplify the complex system, the Kronecker product and its properties are applied to rewrite the complex system. According to whether the transfer function is a multi-proportional delayed function or a single proportional delayed function, several seemly Lyapunov Krasovskii functionals (LKFs) are constructed. Then, through the use of Kronecker product, Green’s formula and inequality analysis method, several criteria of input-strictly passivity (ISP) and output-strictly passivity (OSP) of the studied systems are attained, which all rely on proportional delayed factors. In addition, these criteria are exhibited in the form of matrix inequalities and can be checked with conventional software. Eventually, the passivity criteria are validated by two numerical examples and simulations.

Passivity Analysis for Switched Generalized Delayed Neural Networks

This brief concerns the passivity issue for a class of continuous-time switched generalized neural networks (CSGNNs) with time-varying delay. Note that the existing related results about switched delayed neural networks are based on the time-dependent or the state-dependent switching strategies, where the time-dependent versions require the stability of each subnetwork, while the state-dependent versions can not avoid the frequent switching, chattering and Zeno problems. For handling this situation, the combined switching strategy is introduced on the basis of the constructed time-dependent multiple Lyapunov-Krasovskii functional approach. A new passivity criterion with less conservativeness is formulated, under which the addressed neural networks are passive with a guaranteed switching frequency. Also, each individual subnetwork can be non-passive. Finally, the employed simulation example substantiates the accuracy and superiority of the derived results.

Novel order-dependent passivity conditions of fractional generalized Cohen–Grossberg neural networks with proportional delays

This work delves into the passivity of fractional generalized Cohen–Grossberg neural networks (CGNNs) with proportional delays. In particular, two forms of Lipschitz conditions for activation function are considered. Some passivity criteria are given by utilizing the Schur Complement lemma, Lyapunov–Krasovskii functional approach and Cauchy matrix inequality. The presented conditions are derived as matrix inequality forms and related to the proportional factor and order. This can clearly reflect the influence of the order and proportional factor on the input–output energy of the system. Two examples are particularized to better substantiate the obtained passivity results.

Passivity and passification of fractional-order memristive neural networks with time delays

A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.

Hierarchical Passivity Criterion for Delayed Neural Networks via A General Delay-Product-Type Lyapunov-Krasovskii Functional.

This article is concerned with passivity analysis of neural networks with a time-varying delay. Several techniques in the domain are improved to establish the new passivity criterion with less conservatism. First, a Lyapunov-Krasovskii functional (LKF) is constructed with two general delay-product-type terms which contain any chosen degree of polynomials in time-varying delay. Second, a general convexity lemma without conservatism is developed to address the positive-definiteness of the LKF and the negative-definiteness of its time-derivative. Then, with these improved results, a hierarchical passivity criterion of less conservatism is obtained for neural networks with a time-varying delay, whose size and conservatism vary with the maximal degree of the time-varying delay polynomial in the LKF. It is shown that the conservatism of the passivity criterion does not always reduce as the degree of the time-varying delay polynomial increases. Finally, a numerical example is given to illustrate the proposed criterion and benchmark against the existing results.

Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality

<abstract><p>The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.</p></abstract>

Improved passivity‐based control for Markovian jump singular systems with aperiodic sampling and actuator failures

AbstractThis aricle investigates the passivity‐based control problem for Markovian jump singular systems with aperiodic sampling and actuator failures. Firstly, in order to fully consider the system information, two novel mode‐dependent Lyapunov–Krasovskii functions (LKFs) are constructed, which are composed of one‐sided and two‐sided looped‐functionals respectively. Based on these two LKFs and an improved integral inequality, two stochastic admissibility and robust passivity criteria with lesser conservatism are given by using linear matrix inequalities (LMIs). Moreover, through these theorems, it is proved that the positive constraint of LKFs can be relaxed from all times to sampling times for Markovian jump singular systems with aperiodic sampling and actuator failures. Then, two aperiodic sampled‐data controller algorithms are proposed by LMIs to ensure the stability of the systems. Finally, A numerical example and a model of DC motor driving an inverted pendulum are provided to demonstrate the validity of the main results.

Passivity criteria for controlled affine resistive components

AbstractPassivity criteria for controlled affine resistive (CAR) components are presented. First, the definitions of passive component and non‐dynamic component are recalled, as formulated in the frame of the behavioral approach (i.e., based on the concept of forwards concatenation set of an admissible process at a given time). Then, three lemmas, one theorem, and four corollaries on quadratic functions are stated and proven, which provide the mathematical tools needed. On this basis, passivity criteria for CAR components are derived, under both the standard (i.e., homogeneous, hybrid, and transmission) matrix representations and the general matrix representation. Finally, by resorting to a kind of canonic representation, two general results on the passivity of CAR components are obtained.

A Novel Passivity Criterion for Bilateral Teleoperation Under Event-triggered PD-like Control with Constant Time Delays

A Novel Passivity Criterion for Bilateral Teleoperation Under Event-triggered PD-like Control with Constant Time Delays

Wave equations for porous media described by the Biot model

Single-mode equivalent space-time representations of the acoustic wave propagating in a Biot poroelastic medium have previously been found only for asymptotic cases: In the low frequency regime, where the viscous skin depth is greater than the characteristic pore size, the time domain equivalent is represented with integer order temporal and spatial loss terms, whereas in the high frequency regime, it is represented with fractional order temporal and spatial loss terms. In the current work, a time domain representation in terms of a partial differential equation is proposed for all three wave solutions of the Biot model across all frequencies, and it is derived from the material response function of the Biot poroelastic medium with suitable approximations for the compressional modes and the dynamic permeability. The dynamic permeability in the time domain is represented by a fractional pseudo-differential operator. Optimal correction factors are introduced into the wave equation to compensate for the discrepancies in the compressional wave dispersion and attenuation. Additionally, the method for incorporating the squirt flow mechanism into the wave equation via the Extended Biot poroviscoelastic model is described. The proposed wave equation has a physical basis and satisfies the passivity criterion.

New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach

This paper deals with the problem of finite-time passivity analysis for a class of fractional-order neural networks with constant time delay. Firstly, based on the existing passivity definition, some new concepts namely, finite-time passivity, finite-time input strict passivity, finite-time output strict passivity, and finite-time strict passivity are introduced in terms of Lyapunov function for fractional-order neural networks. In this paper, for the first time, by defining an appropriate controller and by exploiting the introduced definitions, some novel delay-dependent and order-dependent sufficient conditions ensuring the passivity performances are obtained for the addressed system. In addition, the finite-time stability conditions are also presented with an explicit formula for determining the value of setting time for stability. Finally, one numerical example is given to verify the effectiveness of the obtained theoretical results and the simulation results are provided for better understanding of the proposed problem.

Event-triggered passivity and synchronization of coupled reaction–diffusion neural networks with and without time-varying delay

This paper is devoted to deal with the event-triggered passivity and synchronization problems for two types of coupled reaction–diffusion neural networks (CRDNNs). In the first type, several passivity and synchronization criteria for CRDNNs are acquired through designing suitable event-triggered controllers, combining some inequality techniques and Lyapunov functional approach. In the second type, the problems of event-triggered synchronization and passivity for coupled delayed reaction–diffusion neural networks (CDRDNNs) are investigated. Finally, two numerical examples are provided to illustrate the effectiveness of the derived passivity and synchronization conditions.

Feedback Control for Passivity of Memristor-Based Multiple Weighted Coupled Neural Networks

This paper investigates the passivity of multiple weighted coupled memristive neural networks (MWCMNNs) based on the feedback control. Firstly, a kind of memristor-based coupled neural network model with multiple weights is presented for the first time. Furthermore, a novel passivity criterion for MWCMNNs is established by constructing an appropriate Lyapunov functional and developing a suitable feedback controller. In addition, with the assistance of some inequality techniques, sufficient conditions for ensuring the input strict passivity and output strict passivity of MWCMNNs are derived. Finally, the validity of the theoretical results is verified by a numerical example.

Passivity analysis of fractional-order neural networks with interval parameter uncertainties via an interval matrix polytope approach

This paper investigates the passivity analysis problem of a class of fractional-order neural networks with interval parameter uncertainties (FONNs-IPUs). The previous IPU processing methods are mainly divided into three categories, i.e., directly using the maximum upper bound matrix or the minimum lower bound matrix, using the combination of these two matrices, and using the maximum norm bound matrix. These methods have some shortcomings, for example, the coupling of information between different intervals and the effect of the negative sign of connection weight are not considered. In order to better analyze the passivity of FONNs-IPUs, firstly, a novel treatment approach of IPUs called interval matrix polytope is proposed, which considers all possible boundary information matrices and the sign of IPUs. Secondly, based on the interval matrix polytope approach, the passivity criteria of FONNs-IPUs are established in linear matrix inequality forms. Finally, the effectiveness of the theoretical results is illustrated by simulation example.

Robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay

This paper deals with the problem of delay-range-dependent robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. The uncertainties under consideration are norm-bounded uncertainties and the restriction on the derivative of the discrete and distributed interval time-varying delays is removed, which means that a fast interval time-varying delay is allowed. By applying a novel Lyapunov-Krasovskii functional approach, improved integral inequalities, Leibniz-Newton formula and utilization of zero equation, then a new delay-range-dependent passivity criterion of neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay is established in terms of linear matrix inequalities (LMIs). Furthermore, some less conservative delay-dependent passivity criteria are obtained. Moreover, we derived a robust passivity criterion for uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. Besides, a less conservative delay-dependent robust passivity criterion is obtained. Finally, five numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Exponential passivity of discrete-time switched neural networks with transmission delays via an event-triggered sliding mode control

This paper investigates the exponential passivity of discrete-time switched neural networks (DSNNs) with transmission delays via an event-triggered sliding mode control (SMC). Firstly, a novel discrete-time switched SMC scheme is constructed on the basis of sliding mode control method and event-triggered mechanism. Next, a state observer with transmission delays is designed to estimate the system state. Moreover, some new weighted summation inequalities are further proposed to effectively evaluate the exponential passivity criteria for the closed-loop system. Finally, the effectiveness of theoretical results is showed through a simulative analysis on a multi-area power system.