Exponential Stabilization of Inertial Memristive Neural Networks With Multiple Time Delays

Input-to-state stability of delayed memristor-based inertial neural networks via non-reduced order method

This paper is concerned with the input-to-state stability (ISS) for a kind of delayed memristor-based inertial neural networks (DMINNs). Based on the nonsmooth analysis and stability theory, novel delay-dependent and delay-independent criteria on the ISS of DMINNs are obtained by constructing different Lyapunov functions. Moreover, compared with the reduced order approach used in the previous works, this paper consider the ISS of DMINNs via non-reduced order approach. Directly analysis the model of DMINNs can better maintain its physical backgrounds, which reduces the complexity of calculations and is more rigorous in practical application. Additionally, the novel proposed results on the ISS of DMINNs here incorporate and complement the existing studies on memristive neural network dynamical systems. Lastly, a numerical example is provided to show that the obtained criteria are reliable.

Observer-based resilient dissipativity control for discrete-time memristor-based neural networks with unbounded or bounded time-varying delays

This work focuses on the issue of observer-based resilient dissipativity control of discrete-time memristor-based neural networks (DTMBNNs) with unbounded or bounded time-varying delays. Firstly, the Luenberger observer is designed, and additionally based on the observed states, the observer-based resilient controller is proposed. An augmented system is presented by considering both the error system and the DTMBNNs with the controller. Secondly, a novel sufficient extended exponential dissipativity condition is obtained for the augmented system with unbounded time-varying delays by proposing a system solutions-based estimation approach. This method is based on system solutions and without constructing any Lyapunov-Krasovskii functionals (LKF), thereby reducing the complexity of theoretical derivation and computational workload. In addition, an algorithm is proposed to solve the nonlinear inequalities in the sufficient condition. Thirdly, the sufficient extended exponential dissipativity condition for the augmented system with bounded time-varying delays is also obtained. Finally, the effectiveness of the theoretical results is illustrated through two simulation examples.

The Optimization of Control Parameters: Finite-Time Bipartite Synchronization of Memristive Neural Networks With Multiple Time Delays via Saturation Function

This article studies the memristive neural networks with multiple time delays (MNNsMTDs). The topology of networks is signed, which contains both cooperative and competitive relationships. Two controllers without time delays are designed to achieve finite-time bipartite synchronization (FTBS) and practical FTBS (PFTBS) of MNNsMTDs. A novel controller with a saturation function rather than a sign function is proposed to avoid chattering. Along with the Lyapunov function method, some mathematical techniques, and scaling inequalities, some sufficient conditions for FTBS and PFTBS of MNNsMTDs are attained. Besides, this article also concerns fixed-time bipartite synchronization (FXBS) and practical FXBS (PFXBS) of MNNsMTDs. An optimization model is designed to obtain some optimal control parameters. An algorithm based on particle swarm optimization (PSO) is provided to solve this model. Some numerical examples are included to demonstrate the correctness and applicability of the approaches.

Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication

This paper investigates the finite/fixed-time synchronization problem of delayed inertial memristive neural networks (DIMNNs) using interval matrix-based methods within a unified control framework. By employing set-valued mapping and differential inclusion theory, two distinct methods are applied to handle the switching behavior of memristor parameters: the maximum absolute value method and the interval matrix method. Based on these different approaches, two control strategies are proposed to select appropriate control parameters, enabling the system to achieve finite and fixed-time synchronization, respectively. Additionally, the resulting theoretical criteria differ based on the chosen control strategy, with one expressed in algebraic form and the other in the form of linear matrix inequalities (LMIs). Numerical simulations demonstrate that the interval matrix method outperforms the maximum absolute value method in terms of handling memristor parameter switching, achieving faster finite/fixed-time synchronization. Furthermore, the theoretical results are extended to the field of image encryption, where the response system is utilized for decryption and expanding the keyspace.

Finite-Time Stabilization of Competitive Neural Networks With Time-Varying Delays

This article investigates finite-time stabilization of competitive neural networks with discrete time-varying delays (DCNNs). By virtue of comparison strategies and inequality techniques, finite-time stabilization of the underlying DCNNs is analyzed by designing a discontinuous state feedback controller, which simplifies the controller design and proof processes of some existing results. Meanwhile, global exponential stabilization of the DCNNs is provided under a continuous state feedback controller. In addition, global exponential stability of the DCNNs is shown as an M-matrix, which contains some published outcomes as special cases. Finally, three examples are given to illuminate the validity of the theories.

Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks

This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.

Exponential Stabilization for a Class of Strict-Feedback Nonlinear Time Delay Systems via State Feedback Control Scheme

This paper considers the exponential stabilization problem for a class of strict-feedback nonlinear systems with multiple time-varying delays, whose nonlinear terms satisfy the linear growth condition. The state feedback controller that relies on a positive parameter to be determined is constructed to deal with nonlinear terms. By tactfully introducing the Lyapunov–Krasovskii functional with an exponential function and selecting the applicable parameter to be determined, the implementable state feedback controller can be obtained to guarantee that the closed-loop system is exponentially stable. The proposed state feedback control scheme is finally applied to the control design of two-stage chemical reactor system, which illustrates the effectiveness of the control method.

State bounding for fuzzy memristive neural networks with bounded input disturbances

This paper investigates the state bounding problem of fuzzy memristive neural networks (FMNNs) with bounded input disturbances. By using the characters of Metzler, Hurwitz and nonnegative matrices, this paper obtains the exact delay-independent and delay-dependent boundary ranges of the solution, which have less conservatism than the results in existing literatures. The validity of the results is verified by two numerical examples.

Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.

Novel results on finite-time stabilization of state-based switched chaotic inertial neural networks with distributed delays

The p-norm finite-time stabilization (FTS) issue of a class of state-based switched inertial chaotic neural networks (SBSCINNs) with distributed time-varying delays is investigated. By using a suitable variable transformation, such second-order SBSCINNs are turned into the first-order differential equations. Then some novel criteria are obtained to stabilize SBSCINNs in a finite time based on the theory of finite-time control and non-smooth analysis together with designing two proper delay-dependent feedback controllers. Besides, the settling time of FTS is also estimated and discussed. Finally, the validity and practicability of the deduced theoretical results are verified by examples and applications.