Generalization of an input-to-state stability preserving Runge-Kutta method for nonlinear control systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:255

Article

Deflorian, Michael¹  Rungger, Matthias² 

[1] Forsch & Innovat Zentrum, BMW Grp, D-80788 Munich, Germany

[2] Univ Calif Los Angeles, Dept Elect Engn, Los Angeles, CA 90024 USA

关键词: Control systems;    Runge-Kutta methods;    Input-to-state stability;    B-input-to-state stability;    (k, l, m)-algebraic stability;   

DOI  :  10.1016/j.cam.2013.05.017

来源: Elsevier

【 摘 要 】

Given a nonlinear control system that is input-to-state stable (ISS) it is assured that the states of the system remain bounded if the input is bounded and the system is global asymptotic stable (GAS) in the sense of Lyapunov in the absence of inputs. Recently, Hu and Liu (2007) [7] studied under which condition ISS of a continuous time nonlinear control system implies ISS of the discrete time system obtained by an implicit Runge-Kutta (RK) method. In this contribution, we extend those results to explicit RK methods. This represents an important extension with respect to applications like system identification where explicit RK methods are presupposed or real-time applications where the computational burden of implicit RK methods is prohibitive. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free