Stabilization of closed sets for passive systems, part I: Reduction principles

— Given an unforced nonlinear system and two nested closed and invariant sets Γ ⊂ O, we present reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of Γ from analogous properties of the system restricted to O. As a corollary to our reduction principles, we present a stability criterion for cascadeconnected systems which generalizes well-known results in the literature. Using the reduction principles, in Part II of this paper we present a comprehensive theory for passivity-based stabilization of closed sets.

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Mohamed I. El-Hawwary, Manfredi Maggiore
• Keywords: Asymptotic Stability, CDC 2008, Control Systems, Invariant Sets, Reduction Principles