On reduction of differential inclusions and Lyapunov stability
Abstract
In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is pointwise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2020
- Source ID
- 10.1051/cocv/2019074
Entities
People
- Andrew R. Teel
- Rushikesh Kamalapurkar
- Warren E Dixon
Organizations
- Air Force Office of Scientific Research
- Air Force Research Laboratory
- National Science Foundation
- Office of Naval Research