Abstract
This paper presents nonlinear small-gain theorems for input-to-state stability and input-to-output stability properties of large-scale time-delay systems consisting of multiple subsystems based on Razumikhin-type techniques. A key strategy is to follow the spirit of the Razumikhin theorem and treat the state variables with delays as disturbances to the system in question. A consequence of this approach is that the problem of stability analysis for large-scale systems described by functional differential equations is converted into a more tractable one for state-delay-free systems with disturbances.
Original language | English (US) |
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Pages (from-to) | 27-63 |
Number of pages | 37 |
Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |
Volume | 19 |
Issue number | 1 |
State | Published - 2012 |
Keywords
- Input-to-output stability
- Input-to-state stability
- Nonlinear small-gain
- Razumikhin theorems
- Time-delay systems
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics