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A UNIFYING INTEGRAL ISS FRAMEWORK FOR STABILITY OF NONLINEAR CASCADES #
 

Summary: A UNIFYING INTEGRAL ISS FRAMEWORK FOR STABILITY OF
NONLINEAR CASCADES #
MURAT ARCAK + , DAVID ANGELI # , AND EDUARDO SONTAG §
SIAM J. CONTROL OPTIM. c
# 2002 Society for Industrial and Applied Mathematics
Vol. 40, No. 6, pp. 1888--1904
Abstract. We analyze nonlinear cascades in which the driven subsystem is integral input­to­
state stable (ISS), and we characterize the admissible integral ISS gains for stability. This character­
ization makes use of the convergence speed of the driving subsystem and allows a larger class of gain
functions when the convergence is faster. We show that our integral ISS gain characterization unifies
di#erent approaches in the literature which restrict the nonlinear growth of the driven subsystem and
the convergence speed of the driving subsystem. The result is used to develop a new observer­based
backstepping design in which the growth of the nonlinear damping terms is reduced.
Key words. nonlinear cascades, stabilization, integral input­to­state stability
AMS subject classifications. 93C10, 93D05, 93D15, 93D25
PII. S0363012901387987
1. Introduction. Studies on the stabilization of cascade systems have paved
the road to major advances in nonlinear control theory. Among these advances are
several constructive design methods such as backstepping and forwarding, which are
based on recursive applications of cascade designs (see, e.g., Sepulchre, Jankovi’c, and

  

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

 

Collections: Engineering