Non-linear impulsive dynamical systems. Part I: Stability and dissipativity
Authors: Haddad W. M.; Chellaboina V.; Kablar N. A.
Source: International Journal of Control, Volume 74, Number 17, 20 November 2001 , pp. 1631-1658(28)
Publisher: Taylor and Francis Ltd
Key:
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
Abstract:
In this paper we develop Lyapunov and invariant set stability theorems for non-linear impulsive dynamical systems. Furthermore, we generalize dissipativity theory to non-linear dynamical systems with impulsive effects. Specifically, the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time system dynamics and dissipated energy over the resetting instants. Furthermore, extended Kalman–Yakubovich–Popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived. Finally, the framework is specialized to passive and non-expansive impulsive systems to provide a generalization of the classical notions of passivity and non-expansivity for non-linear impulsive systems. These results are used in the second part of this paper to develop extensions of the small gain and positivity theorems for feedback impulsive systems as well as to develop optimal hybrid feedback controllers.Language: English
Document Type: Research article
Key:
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
Click here for Page Help