Exponential Passivity Research Articles

Novel H ∞ performance and delay-dependent exponential passivity for neural networks in response to leakage delay

Novel H ∞ performance and delay-dependent exponential passivity for neural networks in response to leakage delay

Adaptive output feedback control system design for nonlinear systems via neural networks

AbstractAdaptive output feedback control based on output feedback exponential passivity (OFEP) has a simple structure and strong robustness in regard to disturbances and system uncertainties. However, it is difficult for most nonlinear systems to satisfy the conditions of OFEP. Thus, the introduction of a suitable parallel feedforward compensator (PFC) to construct an OFEP‐augmented system with the controlled system has been used, but the control output cannot achieve perfect tracking because of the output of the introduced PFC. As a solution, introducing a feedforward (FF) input to build a 2 degree of freedom (2‐DOF) is a simple and effective way to solve this problem. In this paper, we propose the design schemes for suitable PFC and FF input of nonlinear systems via the use of neural networks (NN), respectively. Besides, to cope with possibly present input disturbances, we also provide a method to achieve disturbance compensation based on NN to reduce their interference. Finally, the effectiveness of all proposed design schemes is confirmed through numerical simulations.

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.

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.

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.

Stabilization of Nonlinear Fornasini–Marchesini Systems

This paper considers the 2D systems described by the Fornasini–Marchesini statespace model. Direct and converse theorems on the exponential stability of such systems are proved in terms of vector Lyapunov functions. The concepts of exponential passivity and a vector storage function are introduced for solving exponential stabilization problems. An example is given to illustrate the efficiency of the new results.

Novel results on passivity and exponential passivity for multiple discrete delayed neutral-type neural networks with leakage and distributed time-delays

This paper investigates the problem of passivity and exponential passivity for neutral-type neural networks (NNNs) with leakage, multiple discrete delay and distributed time-delay, via some novel sufficient conditions. Based on an appropriate Lyapunov-Krasovskii functional (LKF), free weighting matrix approach and some inequality techniques, enhanced passivity criteria for the concerned neural networks is established in the form of Linear matrix inequalities (LMIs). The feasibility of the attained passivity and exponential passivity criterions easily verified by the aid of LMI control toolbox in MATLAB software. Furthermore, we have compared our method with previous one in the existing literature, which depicts its less conservativeness. To substantiate the superiority and effectiveness of our analytical design, two examples with their numerical simulations are provided.

Exponential passivity conditions on neutral stochastic neural networks with leakage delay and partially unknown transition probabilities in Markovian jump

This paper studies the problem of exponential passivity for neutral stochastic neural networks (NSNN) with leakage delay and Markovian jump. The Markovian jump has partially unknown transition probabilities (PUTPs). By utilizing the Itô differential rule, choosing a suitable Lyapunov–Krasovskii functional and combining with the inequality technique, the sufficient delay-dependent exponential passivity criteria are obtained. These sufficient conditions are provided in the form of linear matrix inequalities (LMIs), which can be easily solved by LMI toolbox in Matlab. Finally, two simulated numerical examples are discussed in detail to illustrate the effectiveness of the established results.

Exponential passivity for uncertain neural networks with time-varying delays based on weighted integral inequalities

Abstract This paper is concerned with the problem of an exponential passivity analysis for uncertain neural networks with time-varying delays. By constructing an appropriate Lyapunov–Krasovskii functional and using the weighted integral inequality techniques to estimate its derivative. We established a sufficient criterion such that, for all admissible parameter uncertainties, the neural network is exponentially passive. The derived criteria are expressed in the terms of linear matrix inequalities (LMIs), that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Exponential Feedback Passivity of Switched Polynomial Nonlinear Systems

The exponential feedback passivity problem of switched polynomial nonlinear systems is studied. To obtain this aim, a method of parameterization of controller is presented and parameter solution algorithm is described. Then, the addressed method is utilized to solve the robust stabilization for a class of switched polynomial nonlinear systems with parameter uncertainties and external disturbance. This result extends the previous results on exponential feedback passivity from the case of nonlinear systems to switched nonlinear systems. A numerical example is given to demonstrate the effectiveness of the proposed result.

Stabilization of Two-Dimensional Nonlinear Systems Described by Fornasini--Marchesini and Roesser Models

The paper considers nonlinear two-dimensional systems described by the Fornasini--Marchesini or Roesser state-space models. Conditions for such systems to have a physically motivated exponential stability property are derived using vector Lyapunov functions. A form of passivity, termed exponential passivity, is introduced and used, together with a vector storage function, to develop a feedback based control law that guarantees exponential stability of the controlled system. For cases where noise is present, stochastic dissipativity in the second moment is defined and then a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a feedback based control law such that the controlled system also has this property. Two physically motivated particular cases, a system with nonlinear actuator dynamics and additive noise and a linear system with state-dependent noise, respectively, are also considered to demonstrate the effectiveness of the new results.

Stochastic Stability of Some Classes of Nonlinear 2D Systems

The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a special case of 2D systems that originate from the modeling of physical processes. Using the vector Lyapunov function method, sufficient conditions for stability in the mean square are obtained in the stochastic setting, where the vast majority of the currently known results are for deterministic dynamics. Based on these results, the property of stochastic exponential passivity in the second moment is used, together with the vector storage function, to develop a new method for output feedback control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate the effectiveness of the new results.

New results on passivity analysis of memristive neural networks with time-varying delays and reaction–diffusion term

Abstract In this paper, we put in effort to inspect the passivity and exponential passivity problem of memristive neural networks with time-varying delays and reaction–diffusion term. Based on the basis of generalized Lyapunov approach, Poincar e ` inequality, Schur complement Lemma, free-weighting matrix approach as well as some inequality techniques, the main conclusions of this paper are derived in the form of linear matrix inequality (LMI). What is noteworthy is that the obtained sufficient criteria rely on the reaction–diffusion term, which implies that the reaction–diffusion term can effect the passivity of the given system. Finally, two numerical examples are emerged to check the practicability of the derived passivity conditions.

New exponential passivity of BAM neural networks with time-varying delays

In this paper, the exponential passivity for bidirectional associative memory (BAM) neural networks with time-varying delays is considered. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative or zero. By constructing new and improved Lyapunov–Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential passivity criterion for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). A numerical example is given to show that the derived condition is less conservative than some existing results given in the literature.

Exponential Passivity Results for Singular Networked Cascade Control Systems Via Sampled-Data Control

This paper addresses the issues of admissibility analysis and exponential passivity using sampled-data control for a class of singular networked cascade control systems (NCCSs) with time-varying delays and external disturbances. Based on the new augmented Lyapunov–Krasovskii functional which considers all the available information about the actual sampling pattern, a new set of delay-dependent condition is obtained to ensure the singular networked cascade control systems to be regular, impulse-free, stable, and exponentially passive. Based on the derived condition, the sampled-data control problem is solved and an explicit expression for the desired cascade controller is given. If the given linear matrix inequalities are feasible, then corresponding gain parameters of the designed cascade control will be determined. Finally, a numerical example based on a power plant boiler–turbine system is provided to demonstrate the effectiveness of the developed technique.

Relaxed exponential passivity criteria for memristor-based neural networks with leakage and time-varying delays

This paper investigates the problem of exponential passivity analysis for memristive neural networks with leakage and time-varying delays. Given that the input and output of the considered neural networks satisfy a prescribed passivity-inequality constraint, the more relaxed criteria are established in terms of linear matrix inequalities by employing nonsmooth analysis and Lyapunov method. The relaxations lie in three aspects: first, this obtained criteria do not really require all the symmetric matrices involved in the employed quadratic Lyapunov-Krasovskii functional to be positive definite; second, the activation functions become general; third, the time-varying delay is not needed to be differentiable. Finally, two numerical examples are given to show the effectiveness of the proposed criteria.

Exponential passivity of memristive neural networks with mixed time-varying delays

This paper is concerned with the exponential passivity for memristive neural networks with mixed time-varying delays. Non-positive definite matrices are applied in an appropriate quadratic Lyapunov functional, a new delay-dependent exponential passivity condition is proposed in terms of linear matrix inequalities (LMIs), such that for all admissible delay bounds. The criterion obtained is only composed of four LMIs, hence compared with the existing results, no excessive calculation is needed to solve the passivity issue. Finally, two examples are listed to illustrate the efficiency and accuracy of the theoretical results.

Exponential passivity analysis of stochastic neural networks with leakage, distributed delays and Markovian jumping parameters

This paper deals with the problem of exponential passivity of Markovian jumping stochastic neural networks with leakage and distributed delays. By constructing a proper Lyapunov–Krasovskii functional, utilizing the free-weighting matrix method and some stochastic analysis techniques, we deduce new delay-dependent sufficient conditions that ensure the passivity of the proposed model. These sufficient conditions are computationally efficient and they can be solved numerically by linear matrix inequality (LMI) toolbox in Matlab. Finally, numerical examples are given to verify the effectiveness and the applicability of the proposed results.

Passivity analysis of memristor-based recurrent neural networks with mixed time-varying delays

In this paper, the passivity problem of memristor-based recurrent neural networks (MRNNs) with mixed time-varying delays is investigated. We adopt a switched system to describe the memristor-based recurrent neural network with mixed time-varying delays. By constructing appropriate Lyapunov–Krasovskii functionals, two sufficient conditions for passivity and exponential passivity of MRNNs are established in terms of linear matrix inequalities (LMIs), respectively. An example is given to demonstrate the effectiveness of the obtained results.

Delay-dependent exponential passivity of uncertain cellular neural networks with discrete and distributed time-varying delays

This paper is concerned with the delay-dependent exponential passivity analysis issue for uncertain cellular neural networks with discrete and distributed time-varying delays. By decomposing the delay interval into multiple equidistant subintervals and multiple nonuniform subintervals, a suitable augmented Lyapunov–Krasovskii functionals are constructed on these intervals. A set of novel sufficient conditions are obtained to guarantee the exponential passivity analysis issue for the considered system. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed results.