Robust dissipative control for semilinear Markovian jump distributed parameter systems with time‐varying delay and incomplete transition probabilities

2019 ◽  
Vol 22 (6) ◽  
pp. 2513-2526 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Junwei Lu ◽  
Jingtao Man
Keyword(s):  
Transition Probabilities ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Dissipative Control ◽  
Varying Delay

scholarly journals State Estimation for a Class of Distributed Parameter Systems with Time-Varying Delay over Mobile Sensor–Actuator Networks with Missing Measurements

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 661
Author(s):  
Huansen Fu ◽  
Baotong Cui ◽  
Bo Zhuang ◽  
Jianzhong Zhang
Keyword(s):  
State Estimation ◽  
Distributed Parameter Systems ◽  
Operator Semigroup ◽  
Distributed Parameter ◽  
Time Varying ◽  
Mobile Sensor ◽  
Missing Measurements ◽  
Time Varying Delay ◽  
Sensor Actuator ◽  
Varying Delay

This work proposes a state estimation strategy over mobile sensor–actuator networks with missing measurements for a class of distributed parameter systems (DPSs) with time-varying delay. Initially, taking advantage of the abstract development equation theory and operator semigroup method, this kind of delayed DPSs described by partial differential equations (PDEs) is derived for evolution equations. Subsequently, the distributed state estimators including consistency component and gain component are designed; the purpose is to estimate the original state distribution of the delayed DPSs with missing measurements. Then, a delay-dependent guidance approach is presented in the form of mobile control forces by constructing an appropriate Lyapunov function candidate. Furthermore, by applying Lyapunov stability theorem, operator semigroup theory, and a stochastic analysis approach, the estimation error systems have been proved asymptotically stable in the mean square sense, which indicates the estimators can approximate the original system states effectively when this kind of DPS has time-delay and the mobile sensors occur missing measurements. Finally, the correctness of control strategy is illustrated by numerical simulation results.

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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