A chain observer for nonlinear long constant delay systems: A matrix inequality approach

Automatica ◽  
2016 ◽  
Vol 65 ◽  
pp. 164-169 ◽  
Author(s):  
Alaleh Vafaei ◽  
Mohammad Javad Yazdanpanah
Keyword(s):  
Delay Systems ◽  
Matrix Inequality ◽  
Constant Delay ◽  
A Chain

scholarly journals On time transformations for differential equations with state-dependent delay

2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Alexander Rezounenko
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
The State ◽  
Delay Systems ◽  
Constant Delay ◽  
Systems Of Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Time Transformations

AbstractSystems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

Guaranteed Cost Control of Saturated Time-Varying Delay Systems

2012 ◽  
Vol 235 ◽  
pp. 129-134
Author(s):  
Han Lin He ◽  
Xiao Dong Wang ◽  
Wei Jun Li
Keyword(s):  
Schur Complement ◽  
Controller Synthesis ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Time Varying Delay ◽  
Guaranteed Cost ◽  
Degree Function ◽  
Varying Delay

This paper mainly considers the control problem of saturated time-varying delay systems. Applying the saturation degree function and the convex hull theory to handle the saturated terms, we put forward the guaranteed cost controller of the system according to the Lyapunov-Krasovskii theorem. Then we make use of Schur complement to convert the QMI (quadratic matrix inequality) to a LMI (linear matrix inequality) and so it can be easily used as controller synthesis. Finally, we apply the guaranteed cost controller to a two dimentional time-varying delay cellular neural networks, and the simulation results show the effectiveness of the proposed controller.

scholarly journals Mixed H2/H∞ Control for Itô-type Stochastic Time-Delay Systems with Applications to Clothing Hanging Device

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yan Qi ◽  
Min Zhang ◽  
Zhiguo Yan
Keyword(s):  
Time Delay ◽  
Performance Index ◽  
Closed Loop ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Closed Loop Systems ◽  
Mean Square Stability ◽  
Stochastic Time

This paper deals with the problem of mixed H2/H∞ control for Itô-type stochastic time-delay systems. First, the H2/H∞ control problem for stochastic time-delay systems is presented, which considers the mean square stability, H2 control performance index, and the ability of disturbance attenuation of the closed-loop systems. Second, by choosing an appropriate Lyapunov–Krasoviskii functional and using matrix inequality technique, some sufficient conditions for the existence of state feedback H2/H∞ controller for stochastic time-delay systems are obtained in the form of linear matrix inequalities. Third, two convex optimization problems with linear matrix inequality constraints are formulated to design the optimal mixed H2/H∞ controller which minimizes the guaranteed cost of the closed-loop systems with known and unknown initial functions, and the corresponding algorithm is given to optimize H2/H∞ performance index. Finally, a numerical example is employed to show the effectiveness and feasibility of the proposed method.

scholarly journals Delay-Dependent Stability of Uncertain Distributed Time-Delay Systems

2012 ◽  
Vol 6-7 ◽  
pp. 45-48
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Distributed Time Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality (LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

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