Two conditions concerning common quadratic Lyapunov functions for linear systems

1997 ◽  
Vol 42 (5) ◽  
pp. 719-722 ◽  
Author(s):  
T. Ooba ◽  
Y. Funahashi
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
Quadratic Lyapunov Functions

Cone-Copositive Piecewise Quadratic Lyapunov Functions for Conewise Linear Systems

2015 ◽  
Vol 60 (11) ◽  
pp. 3077-3082 ◽  
Author(s):  
Raffaele Iervolino ◽  
Francesco Vasca ◽  
Luigi Iannelli
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
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.

scholarly journals Adaptive Backstepping Method for Stabilizing Systems of Fractional Order Ordinary Differential Equations

2021 ◽  
Vol 24 (4) ◽  
pp. 46-51
Author(s):  
Asad J. Taher ◽  
◽  
Fadhel S. Fadhel ◽  
Nabaa N. Hasan ◽  
◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Fractional Order ◽  
Lyapunov Functions ◽  
Backstepping Method ◽  
Adaptive Backstepping ◽  
Quadratic Lyapunov Functions ◽  
The Stability

In this paper the method of adaptive backstepping for stabilizing and solving system of ordinary and partial differential equations will be used and applied to investigate and study the stability linear systems of Caputo fractional order ordinary differential equations. The basic idea of this approach is to find a quadratic Lyapunov functions for stabilizing the subsystems.

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