scholarly journals Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Aowen Kong ◽  
Carlos Nonato ◽  
Wenjun Liu ◽  
Manoel Jeremias dos Santos ◽  
Carlos Raposo
Keyword(s):  
Time Dependent ◽  
Exponential Stabilization ◽  
Time Varying ◽  
Observability Inequality ◽  
Time Varying Delay ◽  
Varying Delay

Delay-Dependent Exponential Stabilization for Linear Distributed Parameter Systems With Time-Varying Delay

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Jun-Wei Wang ◽  
Chang-Yin Sun
Keyword(s):  
Time Delay ◽  
Distributed Parameter Systems ◽  
Dirichlet Boundary Conditions ◽  
Exponential Stabilization ◽  
Distributed Parameter ◽  
Control Input ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper extends the framework of Lyapunov–Krasovskii functional to address the problem of exponential stabilization for a class of linearly distributed parameter systems (DPSs) with continuous differentiable time-varying delay and a spatiotemporal control input, where the system model is described by parabolic partial differential-difference equations (PDdEs) subject to homogeneous Neumann or Dirichlet boundary conditions. By constructing an appropriate Lyapunov–Krasovskii functional candidate and using some inequality techniques (e.g., spatial integral form of Jensen's inequalities and vector-valued Wirtinger's inequalities), some delay-dependent exponential stabilization conditions are derived, and presented in terms of standard linear matrix inequalities (LMIs). These stabilization conditions are applicable to both slow-varying and fast-varying time delay cases. The detailed and rigorous proof of the closed-loop exponential stability is also provided in this paper. Moreover, the main results of this paper are reduced to the constant time delay case and extended to the stochastic time-varying delay case, and also extended to address the problem of exponential stabilization for linear parabolic PDdE systems with a temporal control input. The numerical simulation results of two examples show the effectiveness and merit of the main results.

scholarly journals Exponential Stabilization of Neutral-Type Neural Networks with Interval Nondifferentiable and Distributed Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Activation Functions ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

The problem of exponential stabilization of neutral-type neural networks with various activation functions and interval nondifferentiable and distributed time-varying delays is considered. The interval time-varying delay function is not required to be differentiable. By employing new and improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, the stabilizability criteria are formulated in terms of a linear matrix inequalities. Numerical examples are given to illustrate and show the effectiveness of the obtained results.

scholarly journals Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Yali Dong ◽  
Shengwei Mei ◽  
Xueli Wang
Keyword(s):  
Nonlinear Systems ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Riccati Differential Equations ◽  
Continuous State ◽  
Varying Delay

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is considered in the paper. By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. Finally, two numerical examples are given to demonstrate the validity of the results.

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