Semiglobal practical integral input-to-state stability for a family of parameterized discrete-time interconnected systems with application to sampled-data control systems. (August 2015)

• Record Type: Journal Article
• Authors: Noroozi, Navid; Khayatian, Alireza; Karimi, Hamid Reza
• Is Part Of: Nonlinear analysis. Volume 17(2015)
• Page Start: 10
• Page End: 24
• Publication Date: 2015-08
• Subjects: Semiglobal practical input-to-state stability -- Semiglobal practical integral input-to-state stability -- Parameterized discrete-time systems -- Small-gain conditions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2015.01.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Semiglobal practical integral input-to-state stability (SP-iISS) for a feedback interconnection of two discrete-time subsystems is given. We construct a Lyapunov function from the sum of nonlinearly-weighted Lyapunov functions of individual subsystems. In particular, we consider two main cases. The former gives SP-iISS for the interconnected system when both subsystems are semiglobally practically integral input-to-state stable. The latter investigates SP-iISS for the overall system when one of subsystems is allowed to be semiglobally practically input-to-state stable. Moreover, SP-iISS for discrete-time cascades and a feedback interconnection including a semiglobally practically integral input-to-state stable subsystem and a static subsystem are given. As an application of the results, these can be exploited in controller design for a sampled-data system in the framework proposed in Nešić et al. (1999) and Nešić and Angeli (2002). We illustrate such a controller design via an example.