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 ℒ2 stability from a disturbance input acting at the input of the plant to the plant output. ℒ2 stability is established by giving a bound on the corresponding ℒ2 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 Nešić 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). Copyright © 2010 John Wiley & Sons, Ltd.
Analytical and numerical Lyapunov functions for SISO linear control systems with First Order Reset Elements
Zaccarian, Luca;
2011-01-01
Abstract
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 ℒ2 stability from a disturbance input acting at the input of the plant to the plant output. ℒ2 stability is established by giving a bound on the corresponding ℒ2 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 Nešić 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). Copyright © 2010 John Wiley & Sons, Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
