Abstract
Nonlinear scalar equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norms of solutions are established. These estimates give us explicit conditions for the absolute and input-to-state stabilities of the considered equations. The Aizerman-type problem from the theory of absolute stability is also discussed. The suggested approach enables us to consider various classes of systems from the unified point of view.
Original language | English |
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Pages (from-to) | 151-167 |
Number of pages | 17 |
Journal | International Journal of Robust and Nonlinear Control |
Volume | 19 |
Issue number | 2 |
DOIs | |
State | Published - 25 Jan 2009 |
Keywords
- Absolute stability
- Aizerman-type problem
- Causal mappings
- Difference equations with continuous time
- Differential equations
- Functional differential equations
- Input-to-state stability
ASJC Scopus subject areas
- Control and Systems Engineering
- Chemical Engineering (all)
- Biomedical Engineering
- Aerospace Engineering
- Mechanical Engineering
- Industrial and Manufacturing Engineering
- Electrical and Electronic Engineering