A Unifying Integral ISS Framework for Stability of Nonlinear Cascades

Abstract. We analyze nonlinear cascades in which the driven subsystem is integral input-tostate stable (ISS), and we characterize the admissible integral ISS gains for stability. This characterization 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 different 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 observer-based backstepping design in which the growth of the nonlinear damping terms is reduced. Key words. nonlinear cascades, stabilization, integral input-to-state stability AMS subject classifications. 93C10, 93D05, 93D15, 93D25 PII. S0363012901387987

• Type: Journal
• Year: 2002
• Where: SIAMCO
• Authors: Murat Arcak, David Angeli, Eduardo D. Sontag
• Keywords: Integral Iss, Nonlinear Cascades, SIAMCO 2002, Subsystem