Abstract
This paper introduces a notion of distance between nonlinear dynamical systems which is suitable for a quantitative description of the robustness of stability in a feedback interconnection. This notion is one of several possible generalizations of the gap metric, and applies to dynamical systems which possess a differential graph. It is shown that any system which is stabilizable by output feedback, in the sense that the closed-loop system is input-output incrementally stable and possesses a linearization about any operating trajectory (i.e., about any admissible input-output pair), has a differential graph. A system which possesses a differentiable graph is globally differentiably stabilizable if the linearized model about any admissible input-output trajectory is stabilizable. It follows that if a nonlinear dynamical system is globally incrementally stabilizable, then it is (globally incrementally) stabilizable by a linear (possibly time-varying) controller. A suitable notion of a minimal opening between nonlinear differential manifolds is introduced and sufficient conditions guaranteeing robustness of stability are provided.
Original language | English (US) |
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Pages (from-to) | 289-306 |
Number of pages | 18 |
Journal | Mathematics of Control, Signals, and Systems |
Volume | 6 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1993 |
Externally published | Yes |
Keywords
- Gap metric
- Nonlinear systems
- Robust control