The behavior of incrementally stable discrete time systems

✍ Scribed by V. Fromion; G. Scorletti

• Book ID: 104300504
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 163 KB
• Volume: 46
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(02)00164-0

✦ Synopsis

This paper focus on the behavior analysis of incrementally bounded (Lipschitz continuous) systems on lp with p ∈ [1; ∞). We ÿrst establish the properties of the motions, which are associated with all inputs inside l e p with respect to a modiÿcation of the initial condition. As a matter of fact, under some minimality properties of the state-space realization of the system, we prove the Lyapunov stability of all unperturbed motions.

As a second point, we investigate the properties of the motions obtained when the input is perturbed, either by perturbations which go to zero at the inÿnity, or by perturbations with a bounded magnitude.

All these results are obtained through the reformulation of the incremental boundedness of a system in terms of the dissipativity of an associated ÿctitious system.