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.

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.

scholarly journals Anti-Saturation Control of Uncertain Time-Delay Systems with Actuator Saturation Constraints

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 375
Author(s):  
Hejun Yao
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Saturation Control ◽  
Systems Model

The problem of anti-saturation control for a class of time-delay systems with actuator saturation is considered in this paper. By introducing appropriate variable substitution, a new delay time-delay systems model with actuator saturation systems is established. Based on the Lyapunov stability theory, the stability condition and the anti-saturation controller design method are obtained by using the linear matrix inequality approach. By introducing the matrix into the Lyapunov function, the proposed conditions are less conservative than the previous results. Finally, a simulation example shows the validity and rationality of the method.

Two term composite nonlinear feedback controller design for nonlinear time-delay systems

2017 ◽  
Vol 40 (12) ◽  
pp. 3424-3432 ◽  
Author(s):  
Sonal Singh ◽  
Shubhi Purwar ◽  
Abhijit Kulkarni
Keyword(s):  
Time Delay ◽  
Transient Response ◽  
Control Technique ◽  
Delay Systems ◽  
Time Delay Systems ◽  
State Control ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Fast Transient Response ◽  
Fast Transient

A two term composite nonlinear feedback (2TCNF) control technique is developed here for nonlinear time delay systems in presence of input saturation. The proposed controller consists of two terms that are conventional composite nonlinear feedback (CNF) control and delay state control. CNF control has advantage of fast transient response and delay state control improves damping characteristics. The proposed controller thus has both these advantages and it tracks the reference smoothly. The closed loop asymptotic stability is guaranteed via Lyapunov–Krasovskii analysis. The efficiency of the proposed controller is tested on exothermic chemical reactor and validated through simulation results. Its performance is compared with the conventional CNF control. The superiority of 2TCNF is established in terms of less overshoot, fast transient response and reduced steady state error.

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 Exponential Estimates and Stabilization of Discrete-Time Singular Time-Delay Systems Subject to Actuator Saturation

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Jinxing Lin
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Decay Rate ◽  
Discrete Time ◽  
Actuator Saturation ◽  
Singular Systems ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Exponential Estimates ◽  
Singular Time

This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

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.

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