Composite quadratic Lyapunov functions for constrained control systems

2003 ◽  
Author(s):  
Tingshu Hu ◽  
Zongli Lin
Keyword(s):  
Control Systems ◽  
Lyapunov Functions ◽  
Constrained Control ◽  
Quadratic Lyapunov Functions

Lanekeeping at the Limits of Handling: Stability via Lyapunov Functions and a Comparison With Stability Control

2008 ◽  
Author(s):  
Kirstin L. R. Talvala ◽  
J. Christian Gerdes
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Lyapunov Functions ◽  
Stability Control ◽  
Tire Model ◽  
Quadratic Lyapunov Functions ◽  
Two Systems ◽  
Assistance Systems ◽  
Safety Systems

Lanekeeping assistance systems and stability control systems both seek to control the yaw behavior of the vehicle. However, lanekeeping systems are typically thought of as linear systems, while stability control systems are explicitly designed to work at the limits of handling. In order to bring these two systems together, there is a need to investigate lanekeeping up to and beyond the limits of handling. This paper presents a nonlinear tire model suitable for analyzing the behavior of a lanekeeping system at all points along the tire curve and a method for finding common quadratic Lyapunov functions to prove stability. The results show that the lanekeeping system is stable well into the nonlinear tire region. This stability holds even under changes in the lanekeeping gain and the understeering/oversteering characteristics of the vehicle. The results suggest that future safety systems could benefit from incorporating integrated lanekeeping and stability control functionality.

Piecewise quadratic Lyapunov functions for linear control systems with First Order Reset Elements

2010 ◽  
Vol 43 (14) ◽  
pp. 807-812 ◽  
Author(s):  
Thomas Loquen ◽  
Dragan Nesic ◽  
Christophe Prieur ◽  
Sophie Tarbouriech ◽  
Andrew R. Teel ◽  
...  
Keyword(s):  
Control Systems ◽  
Lyapunov Functions ◽  
Linear Control ◽  
Linear Control Systems ◽  
First Order ◽  
Quadratic Lyapunov Functions
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