scholarly journals Lyapunov functional for a linear system with two delays both retarded and neutral type

2010 ◽  
Vol 20 (1) ◽  
Author(s):  
Józef Duda
Keyword(s):  
Linear System ◽  
Lyapunov Functional ◽  
Neutral Type ◽  
Two Delays

scholarly journals Parametric optimization of neutral linear system with two delays with P-controller

2011 ◽  
Vol 21 (4) ◽  
pp. 363-372 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Linear System ◽  
Performance Index ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Neutral Type ◽  
Neutral System ◽  
Initial State ◽  
Quadratic Performance Index ◽  
Two Delays ◽  
Quadratic Performance

Parametric optimization of neutral linear system with two delays with P-controller In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.

scholarly journals Parametric optimization of a neutral system with two delays and PD-controller

2013 ◽  
Vol 23 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Performance Index ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Neutral Type ◽  
Neutral System ◽  
Pd Controller ◽  
Initial State ◽  
Two Delays ◽  
Index Value ◽  
A Performance

In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of discussed theory is presented. It concerns the system with a PD-controller designed to control a plant with two delays both retarded and neutral type. For such system a value of considered performance index is determined.

EXPONENTIAL STABILITY FOR STOCHASTIC NEURAL NETWORKS OF NEUTRAL TYPE WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (11) ◽  
pp. 1099-1110 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
R. SAMIDURAI ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Stochastic Analysis ◽  
Lyapunov Functional ◽  
Neutral Type ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Matrix Inequality

This paper is concerned with the exponential stability of stochastic neural networks of neutral type with impulsive effects. By employing the Lyapunov functional and stochastic analysis, a new stability criterion for the stochastic neural network is derived in terms of linear matrix inequality. A numerical example is provided to show the effectiveness and applicability of the obtained result.

Delayed-Decomposition Approach for Absolute Stability of Neutral-Type Lurie Control Systems With Time-Varying Delays

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Control Systems ◽  
Lyapunov Functional ◽  
Absolute Stability ◽  
Neutral Type ◽  
Upper Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Decomposition Approach ◽  
Delay Dependent

The problem of absolute stability for a class of neutral-type Lurie control system with nonlinearity located in an infinite sector and in a finite one is investigated in this paper. Based on the delayed-decomposition approach (DDA), a new augmented Lyapunov functional is constructed and the delay dependent conditions for asymptotic stability are derived by applying an integral inequality approach (IIA) in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

scholarly journals Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2231
Author(s):  
Jian Zhang ◽  
Ancheng Chang ◽  
Gang Yang
Keyword(s):  
Neural Networks ◽  
Stability Criterion ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Multiple Delays ◽  
Application Range ◽  
Research Article ◽  
Sufficient Stability ◽  
Inertial Neural Networks

The classical Hopefield neural networks have obvious symmetry, thus the study related to its dynamic behaviors has been widely concerned. This research article is involved with the neutral-type inertial neural networks incorporating multiple delays. By making an appropriate Lyapunov functional, one novel sufficient stability criterion for the existence and global exponential stability of T-periodic solutions on the proposed system is obtained. In addition, an instructive numerical example is arranged to support the present approach. The obtained results broaden the application range of neutral-types inertial neural networks.

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