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Power characterizations of input-to-state stability and integral input-to-state stability

Summary: Power characterizations of input-to-state stability and integral
input-to-state stability
D. Angeli
Dip. sistemi e Informatica, Universita di Firenze,
Via di Santa Marta 3, 50139 Firenze, Italy
D. Nesic
Department of Electrical and Electronic Engineering,
The University of Melbourne
Parkville, 3010, Victoria, Australia
New notions of external stability for nonlinear systems are introduced, making use of average powers
as signal norms and comparison functions as in the Input-to-State Stability (ISS) framework. Several
new characterizations of ISS and integral ISS are presented in terms of the new notions. An example is
discussed to illustrate di erences and similarities of the newly introduced properties.
1 Introduction
The notion of input-to-state stability (ISS) has been now widely recognized and accepted as an important
concept that is useful for a range of nonlinear control problems (see [4, 5, 6]). Since its conception in [11] a
range of important equivalent characterizations of ISS have been proved in the literature (see [9, 10, 11, 12,
13]). These characterizations lead to a better understanding of the ISS property and provided the control
engineers with a range of new tools that can be used in nonlinear control. ISS has been originally de ned


Source: Angeli, David - Dipartimento di Sistemi e Informatica, UniversitÓ degli Studi di Firenze


Collections: Engineering