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.

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.

Sliding Mode H∞-Control with Stochastic Time Delay Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1712-1718
Author(s):  
Ravi Kumar ◽  
Kil To Chong
Keyword(s):  
Time Delay ◽  
Sliding Mode ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Linear Filter ◽  
Time Delay Systems ◽  
Stochastic Time

In this paper, we concerned the problem of sliding mode of-control with stochastic stabilization of uncertainty. Some sufficient conditions are derived for this class of robust feedback stabilization of time delay systems. The stochastic time delay systems may switch from one to one corresponds of linear filter, such that the dynamics of estimation error is guaranteed to be stochastically stable in mean square. Moreover, it is shown that for a class of special linear stochastic neutral systems, the H-sliding mode control design can be obtained by solving linear matrix inequalities (LMIs).

scholarly journals Robust Exponential Stabilization of Uncertain Impulsive Bilinear Time-Delay Systems with Saturating Actuators

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Shujie ◽  
Shi Bao ◽  
Zhang Qiang ◽  
Pan Tetie
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Dynamics ◽  
Saturating Actuators ◽  
Robust Exponential Stabilization

This paper investigates the problem of robust exponential stabilization for uncertain impulsive bilinear time-delay systems with saturating actuators. By using the Lyapunov function and Razumikhin-type techniques, two classes of impulsive systems are considered: the systems with unstable discrete-time dynamics and the ones with stable discrete-time dynamics. Sufficient conditions for robust stabilization are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the theoretical results.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

2020 ◽  
pp. 2130001
Author(s):  
Chaibi Noreddine ◽  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Bensalem Boukili
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Varying Delay ◽  
Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

H∞ Constrained Pareto Suboptimal Strategy for Stochastic LPV Time-Delay Systems

2021 ◽  
pp. 2150010
Author(s):  
Hiroaki Mukaidani ◽  
Hua Xu ◽  
Weihua Zhuang
Keyword(s):  
Time Delay ◽  
Dynamic Games ◽  
Sufficient Conditions ◽  
Existence Condition ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Bounded Real Lemma ◽  
State Delays

Not only in control problems, but also in dynamic games, several sources of performance degradation, such as model variation, deterministic and stochastic uncertainties and state delays, need to be considered. In this paper, we present an [Formula: see text] constrained Pareto suboptimal strategy for stochastic linear parameter-varying (LPV) time-delay systems involving multiple decision makers. The goal of developing the [Formula: see text] constrained Pareto suboptimal strategy set is to construct a memoryless state feedback strategy set, so that the closed-loop stochastic LPV system is stochastically mean-square stable. In the paper, the existence condition of the extended bounded real lemma is first established via linear matrix inequalities (LMIs). Then, a quadratic cost bound for cost performance is derived. Based on these preliminary results, sufficient conditions for the existence of such a strategy set under the [Formula: see text] constraint are derived by using cross-coupled bilinear matrix inequalities (BMIs). To determine the strategy set, a viscosity iterative scheme based on the LMIs is established to avoid the processing of BMIs. Finally, two numerical examples are presented to demonstrate the reliability and usefulness of the proposed method.

scholarly journals Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2441
Author(s):  
Chun-Tang Chao ◽  
Ding-Horng Chen ◽  
Juing-Shian Chiou
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Takagi Sugeno

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

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.

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

2006 ◽  
Vol 129 (1) ◽  
pp. 83-90 ◽  
Author(s):  
Shinn-Horng Chen ◽  
Jyh-Horng Chou ◽  
Liang-An Zheng
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Time Delay System ◽  
The Stability ◽  
Singular Time

In this paper, the regional eigenvalue-clustering robustness problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside certain specified regions, two new sufficient conditions are proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle, the proposed criteria will become the stability robustness criteria. For the case of eigenvalue clustering in a specified circular region, one proposed sufficient condition is mathematically proved to be less conservative than those reported very recently in the literature. Another new sufficient condition is also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties holds the properties of regularity, causality, and eigenvalue clustering in a specified region. An example is given to demonstrate the applicability of the proposed sufficient conditions.

scholarly journals Adaptive Output Feedback Sliding Mode Control for Complex Interconnected Time-Delay Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Van Van Huynh ◽  
Yao-Wen Tsai ◽  
Phan Van Duc
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Output Feedback ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Order System ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Mode Control

We extend the decentralized output feedback sliding mode control (SMC) scheme to stabilize a class of complex interconnected time-delay systems. First, sufficient conditions in terms of linear matrix inequalities are derived such that the equivalent reduced-order system in the sliding mode is asymptotically stable. Second, based on a new lemma, a decentralized adaptive sliding mode controller is designed to guarantee the finite time reachability of the system states by using output feedback only. The advantage of the proposed method is that two major assumptions, which are required in most existing SMC approaches, are both released. These assumptions are (1) disturbances are bounded by a known function of outputs and (2) the sliding matrix satisfies a matrix equation that guarantees the sliding mode. Finally, a numerical example is used to demonstrate the efficacy of the method.

Sign in / Sign up

Export Citation Format

Share Document