Title :

On boundedness of solutions of state periodic systems: a multivariable cell structure approach

Author(s) :

Efimov, Denis [Auteur]
Finite-time control and estimation for distributed systems [VALSE]
Schiffer, Johannes [Auteur]
Brandenburg University of Technology [Cottbus – Senftenberg] [BTU]

Journal title :

IEEE Transactions on Automatic Control
64

Pages :

4094−4104

Publisher :

Institute of Electrical and Electronics Engineers

Publication date :

2019-10-01

ISSN :

0018-9286

HAL domain(s) :

Sciences de l'ingénieur [physics]/Automatique / Robotique

English abstract : [en]

Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there ...
Show more >Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability (ISS), i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL