scholarly journals An LMI Approach to Nonlinear State-Feedback Stability of Uncertain Time-Delay Systems in the Presence of Lipschitzian Nonlinearities

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1883
Author(s):  
Mehdi Golestani ◽  
Saleh Mobayen ◽  
S. Hassan HosseinNia ◽  
Saeed Shamaghdari
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
State Feedback ◽  
State Feedback Control ◽  
System Stability ◽  
Control Technique ◽  
Delay Systems ◽  
Feedback Stability ◽  
System Uncertainties ◽  
Nonlinear State

This article proposes a new nonlinear state-feedback stability controller utilizing linear matrix inequality (LMI) for time-delay nonlinear systems in the presence of Lipschitz nonlinearities and subject to parametric uncertainties. Following the Lyapunov–Krasovskii stabilization scheme, the asymptotic stability criterion resulted in the LMI form and the nonlinear state-feedback control technique was determined. Due to their significant contributions to the system stability, time delays and system uncertainties were taken into account while the suggested scheme was designed so that the system’s stabilization was satisfied in spite of time delays and system uncertainties. The benefit of the proposed method is that not only is the control scheme independent of the system order, but it is also fairly simple. Hence, there is no complexity in using the proposed technique. Finally, to justify the proficiency and performance of the suggested technique, a numerical system and a rotational inverted pendulum were studied. Numerical simulations and experimental achievements prove the efficiency of the suggested control technique.

The Motor Active Flexible Suspension and Its Dynamic Effect on the High-Speed Train Bogie

2017 ◽  
Vol 140 (6) ◽  
Author(s):  
Yuan Yao ◽  
Yapeng Yan ◽  
Zhike Hu ◽  
Kang Chen
Keyword(s):  
Control System ◽  
Time Delay ◽  
High Speed ◽  
State Feedback ◽  
State Feedback Control ◽  
System Stability ◽  
High Speed Train ◽  
Suspension Parameters ◽  
Linear And Nonlinear ◽  
Hunting Stability

We put forward the motor active flexible suspension and investigate its dynamic effects on the high-speed train bogie. The linear and nonlinear hunting stability are analyzed using a simplified eight degrees-of-freedom bogie dynamics with partial state feedback control. The active control can improve the function of dynamic vibration absorber of the motor flexible suspension in a wide frequency range, thus increasing the hunting stability of the bogie at high speed. Three different feedback state configurations are compared and the corresponding optimal motor suspension parameters are analyzed with the multi-objective optimal method. In addition, the existence of the time delay in the control system and its impact on the bogie hunting stability are also investigated. The results show that the three control cases can effectively improve the system stability, and the optimal motor suspension parameters in different cases are different. The direct state feedback control can reduce corresponding feed state's vibration amplitude. Suppressing the frame's vibration can significantly improve the running stability of bogie. However, suppressing the motor's displacement and velocity feedback are equivalent to increasing the motor lateral natural vibration frequency and damping, separately. The time delay over 10 ms in control system reduces significantly the system stability. At last, the effect of preset value for getting control gains on the system linear and nonlinear critical speed is studied.

scholarly journals Global State-Feedback Control for Switched Nonlinear Time-Delay Systems via Dynamic Gains

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hui Ye ◽  
Bin Jiang ◽  
Hao Yang ◽  
Gui-Hua Zhao
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Global State ◽  
Switching Law ◽  
Power Integrator ◽  
Dynamic Gain

In this paper, the problem of global state-feedback control is investigated for a class of switched nonlinear time-delay systems. In order to obtain a less-conservative common dynamic gain update law across subsystems, we construct different dynamic gain update laws for individual subsystems. Based on multiple Lyapunov function approach and adding one power integrator technique, the delay-independent controllers for all subsystems and a proper switching law are designed to guarantee that the states of the switched nonlinear time-delay systems can be globally asymptotically to the origin; meanwhile, all the signals of the closed-loop system are bounded. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

scholarly journals Adaptive NN State-Feedback Control for Stochastic High-Order Nonlinear Systems with Time-Varying Control Direction and Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Huifang Min ◽  
Na Duan
Keyword(s):  
State Feedback ◽  
Dynamic Surface Control ◽  
High Order ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Control Technique ◽  
Delay Systems ◽  
Time Varying ◽  
Dynamic Surface ◽  
Control Direction

Nussbaum-type gain function and neural network (NN) approximation approaches are extended to investigate the adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear time-delay systems. The distinct features of this paper are listed as follows. Firstly, the power order condition is completely removed; the restrictions on system nonlinearities and time-varying control direction are greatly weakened. Then, based on Lyapunov-Krasovskii function and dynamic surface control technique, an adaptive NN controller is constructed to render the closed-loop system semiglobally uniformly ultimately bounded (SGUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed control scheme.

Sign in / Sign up

Export Citation Format

Share Document