TY - GEN

T1 - Differential stability and robust control of nonlinear systems

AU - Georgiou, Tryphon T.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - 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, has a differential graph. A system with a differentiable graph is globally differentiably stabilizable if the linearized model about any bounded input/output trajectory is stabilizable. It is shown 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.

AB - 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, has a differential graph. A system with a differentiable graph is globally differentiably stabilizable if the linearized model about any bounded input/output trajectory is stabilizable. It is shown 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.

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M3 - Conference contribution

AN - SCOPUS:0027810880

SN - 0780312988

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 984

EP - 989

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)

Y2 - 15 December 1993 through 17 December 1993

ER -