Exponential stabilization of systems with time-varying delay by periodically intermittent control

2016 ◽  
Author(s):  
Zhiming Zhang ◽  
Yong He ◽  
Min Wu ◽  
Liming Ding
Keyword(s):  
Exponential Stabilization ◽  
Intermittent Control ◽  
Time Varying ◽  
Periodically Intermittent Control ◽  
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.

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