Analytical and numerical Lyapunov functions for SISO linear control systems with first-order reset elements

作者：Zaccarian Luca^*; Nesic Dragan; Teel Andrew R

来源：International Journal of Robust and Nonlinear Control, 2011, 21(10): 1134-1158.

DOI：10.1002/rnc.1649

• reset systems
• Lyapunov stability
• first-order reset elements

In this paper we provide analytical and numerical Lyapunov functions that prove stability and performance of a First-order Reset Element (FORE) in feedback interconnection with a SISO linear plant. The Lyapunov functions also allow to establish finite gain L(2) stability from a disturbance input acting at the input of the plant to the plant output. L(2) stability is established by giving a bound on the corresponding L(2) gains. The proof of stability and performance is carried out by showing that the Lyapunov functions constructed here satisfy the sufficient conditions in the main results of Nesic et al. (Automatica 2008; 44(8): 2019-2026). In the paper we also point out and illustrate via a counterexample an analysis subtlety overlooked in the preliminary results of Zaccarian et al. (American Control Conference, Portland, OR, U. S. A., 2005).

• 出版日期2011-7-10