Linear Quadratic Nash Game of Stochastic Singular Time-Delay Systems with Multiple Decision Makers

2015 ◽  
Vol 3 (5) ◽  
pp. 472-480
Author(s):  
Huainian Zhu ◽  
Guangyu Zhang ◽  
Chengke Zhang ◽  
Ying Zhu ◽  
Haiying Zhou
Keyword(s):  
Time Delay ◽  
Decision Makers ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Linear Quadratic ◽  
Nash Game ◽  
Multiple Decision Makers ◽  
Nash Strategies ◽  
Singular Time

AbstractThis paper discusses linear quadratic Nash game of stochastic singular time-delay systems governed by Itô’s differential equation. Sufficient condition for the existence of Nash strategies is given by means of linear matrix inequality for the first time. Moreover, in order to demonstrate the usefulness of the proposed theory, stochastic H2∕H∞control with multiple decision makers is discussed as an immediate application.

Low-conservative robust composite nonlinear feedback control for singular time-delay systems

2020 ◽  
pp. 107754632095373
Author(s):  
Emad Jafari ◽  
Tahereh Binazadeh
Keyword(s):  
Time Delay ◽  
Actuator Saturation ◽  
Linear Part ◽  
Feedback Controller ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Singular Time

A low-conservative composite nonlinear feedback controller is proposed for singular time-delay systems with time-varying delay. The proposed composite nonlinear feedback controller not only improves the transient responses of the closed-loop system but it also has less conservatism than other composite nonlinear feedback controllers. The gain of the linear part of the composite nonlinear feedback controller is obtained by precise mathematical calculation to depend not only on the upper bound of the delay but also on the delay range and rate of its changes. More advantages of the proposed composite nonlinear feedback controller are its accurate operation in the presence of actuator saturation, model uncertainties, and system singularities. The linear and nonlinear parts of the proposed controller are designed by solving a linear matrix inequality problem confirmed through a theorem using Lyapunov stability analysis. The theoretical achievements are endorsed by computer simulation through numerical and practical examples.

H∞ filter design for singular time-delay systems

2009 ◽  
Vol 223 (7) ◽  
pp. 1001-1015 ◽  
Author(s):  
Z Wu ◽  
H Su ◽  
J Chu
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Lmi Approach ◽  
Delay Dependent ◽  
Filtering Problem ◽  
Singular Time

This paper aims to solve the H∞ filtering problem for singular time-delay systems. Two new and improved delay-dependent bounded real lemmas (BRLs), which are equivalent to each other, are proposed. Based on one of them, an H∞ filter is designed via a linear matrix inequality (LMI) approach. Numerical examples are given to illustrate that the newly proposed methods introduce less conservatism than the existing ones.

scholarly journals Delay-DependentH∞Filtering for Singular Time-Delay Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Zhenbo Li ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Error System ◽  
Cone Complementarity Linearization ◽  
Delay Dependent ◽  
Singular Time

This paper deals with the problem of delay-dependentH∞filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribedH∞performanceγis given in terms of linear matrix inequalities (LMIs). Then, the sufficient condition is obtained for the existence of theH∞filter, and the explicit expression for the desiredH∞filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.

A delay-range-dependent stabilization of uncertain singular time-delay systems with one-sided Lipschitz nonlinearities subject to input saturation

2018 ◽  
Vol 25 (4) ◽  
pp. 868-881 ◽  
Author(s):  
Maryam Sadat Asadinia ◽  
Tahereh Binazadeh ◽  
Behrouz Safarinejadian
Keyword(s):  
Time Delay ◽  
Singular Systems ◽  
Singular System ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Analysis And Design ◽  
Singular Time

This paper investigates the problem of delay-range-dependent robust stabilization for nonlinear singular systems with time-delay subject to some constraints. In practice, the control problem of dynamic systems faces a variety of constraints such as: presence of input saturation; one-sided Lipschitz nonlinearities; model uncertainties; and time-varying delay. The interaction of both algebraic and differential equations in singular systems with delayed state variables adds some complexities and difficulties in the procedure of analysis and design of singular time-delay systems. Moreover, the one-sided Lipschitz nonlinearity condition, which is less conservative than the well-known Lipschitz condition, is considered while the presence of actuator saturation also imposes additional complexity in the procedure of controller design. In this regard, by choosing an appropriate Lyapunov–Krasovskii functional with applying the free-weighting matrices approach, the sufficient conditions are derived as linear matrix inequalities which guarantee the asymptotic stability of the resulting uncertain closed-loop singular system. Finally, computer simulations are provided to verify the theoretical results.

scholarly journals New delay-dependent observer-based control for uncertain stochastic time-delay systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiu-feng Miao ◽  
Long-suo Li
Keyword(s):  
Time Delay ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Noise Disturbances ◽  
System States ◽  
Delay Dependent ◽  
Stochastic Time

AbstractThis paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

scholarly journals New observer-based control design for mismatched uncertain systems with time-delay

2016 ◽  
Vol 26 (4) ◽  
pp. 597-610 ◽  
Author(s):  
Van Van Huynh
Keyword(s):  
Time Delay ◽  
Estimation Error ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
State Matrix ◽  
Control Techniques ◽  
Uncertain Time

Abstract In this paper, the state estimation problem for a class of mismatched uncertain time-delay systems is addressed. The estimation uses observer-based control techniques. The mismatched uncertain time-delay systems investigated in this study include mismatched parameter uncertainties in the state matrix and in the delayed state matrix. First, based on a new lemma with appropriately choosing Lyapunov functional, new results for stabilization of mismatched uncertain time-delay systems are provided on the basis of a linear matrix inequality (LMI) framework and the asymptotic convergence properties for the estimation error is ensured. Second, the control and observer gains are given from single LMI feasible solution which can overcome the drawback of the bilinear matrix inequalities approach often reported in the literature. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.

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