Robust mixed H2 and passive switching control for uncertain discrete switched systems with time delay

2019 ◽  
Vol 37 (2) ◽  
pp. 422-440 ◽  
Author(s):  
Chang-Hua Lien ◽  
Ker-Wei Yu ◽  
Hao-Chin Chang
Keyword(s):  
Time Delay ◽  
Switched Systems ◽  
Switching Control ◽  
Delay System ◽  
Lyapunov Theory ◽  
Linear Matrix ◽  
Time Delay System ◽  
Wirtinger Inequality ◽  
Discrete Time Delay ◽  
Discrete Switched Systems

Abstract In this paper, the problem of mixed ${H}_2$ and passive switching control of uncertain discrete time-delay switched systems is investigated via a switching signal selection. Lyapunov theory with Wirtinger inequality is applied to guarantee the mixed performance for discrete switched time-delay system. The used Linear Matrix Inequality variables are less than our past proposed results. Finally, the improvement of the developed results is illustrated via a numerical example.

A Design of Control Strategy for Chaotic Systems with Time-Delay

2014 ◽  
Vol 541-542 ◽  
pp. 1248-1255
Author(s):  
Jiang Xu ◽  
Tao Li
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Fixed Points ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Delay System ◽  
Delayed Feedback Control ◽  
Time Delay System ◽  
Discrete Time Delay ◽  
Odd Number Limitation

In various kinds of feedback control, delayed control is an important topic for chaos control, which deserves more thorough researches. However, only a few researchers take in to account that whether the delayed feedback control (DFC) can be employed to control chaotic systems with time-delay. To investigate the control strategy, a stabilization problem of unstable fixed points in the discrete time-delay system is taken into considerations in this paper. Based on our conclusion, it is obvious that the odd number limitation property existing in the system without delay also exists in the time-delay one while the DFC is employed to stabilize the unstable fixed points. Second, based on the property of the root-locus diagram, a developed DFC strategy is proposed to release the limitation. The numerical simulation results validate the effectiveness of our design and are in agreement of our analysis.

scholarly journals Synchronization approach for chaotic time-varying delay system based on Wirtinger inequality

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668902
Author(s):  
Zhanshan Zhao ◽  
Meili He ◽  
Jing Zhang ◽  
Guowei Xu
Keyword(s):  
Time Delay ◽  
Stability Criterion ◽  
Delay System ◽  
Jensen Inequality ◽  
Time Delay System ◽  
Control Approach ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Varying Delay

A novel control approach based on Wirtinger inequality is designed for nonlinear chaos synchronization time delay system. In order to reduce the conservatism for the stability criterion, a Lyapunov–Krasovskii functional with triple-integral term is constructed. The improved Wirtinger inequality is used to reduce the conservative which is caused by Jensen inequality, and a stability criterion is proposed by reciprocally convex method. Furthermore, a state feedback controller is designed to synchronize the master-slave systems based on the proposed criteria through cone complementary linearization approach. Finally, a simulation for Lorenz chaos time delay system is given to prove the validity based on the proposed synchronization control approach.

scholarly journals Passivity analysis and synthesis for uncertain time-delay systems

2001 ◽  
Vol 7 (5) ◽  
pp. 455-484 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Lihua Xie
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Delay System ◽  
Passivity Analysis ◽  
Analysis And Synthesis ◽  
Uncertain Time

In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time-delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay-independent and delay-dependent cases are considered. For the synthesis problem, we propose an observer-based design method which guarantees that the closed-loop uncertain time-delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.

scholarly journals H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sha-sha Li ◽  
Zhan-shan Zhao ◽  
Jing Zhang ◽  
Jie Sun ◽  
Lian-kun Sun
Keyword(s):  
Coronary Artery ◽  
Time Delay ◽  
Integral Inequality ◽  
Controller Design ◽  
Convex Combination ◽  
External Disturbance ◽  
Delay System ◽  
Linear Matrix ◽  
Time Delay System ◽  
Input Time

The issue of H∞ control for the coronary artery input time-delay system with external disturbance is of concern. To further reduce conservation, we utilize the free-matrix-based integral inequality, Wirtinger-based integral inequality, and reciprocal convex combination approach to construct Lyapunov-Krasovskii function (LKF). Then a sufficient condition for controller design which can guarantee robust synchronization the coronary artery system is represented in terms of linear matrix inequality (LMI). Finally, a numerical example is exploited to show the effectiveness of the proposed methods.

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