Small-gain theorem for ISS systems and applications. (English) Zbl 0836.93054
A concept of input-to-output practical stability of smooth nonlinear control systems is introduced. A generalized small-gain theorem and a gain assignment theorem are proved. Applications are obtained:
– A sufficient condition for global asymptotic stability (in the spirit of the center manifold reduction theorem);
– Sufficient conditions for global asymptotic stabilization (via partial-state feedback) for linear systems with nonlinear stable dynamic perturbations and for a class of nonlinear control systems composed of a chain of dynamically perturbed integrators.
– A sufficient condition for global asymptotic stability (in the spirit of the center manifold reduction theorem);
– Sufficient conditions for global asymptotic stabilization (via partial-state feedback) for linear systems with nonlinear stable dynamic perturbations and for a class of nonlinear control systems composed of a chain of dynamically perturbed integrators.
Reviewer: M.I.Krastanov (Sofia)
MSC:
| 93D25 | Input-output approaches in control theory |
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
Keywords:
input-to-output practical stability; nonlinear; small-gain theorem; global asymptotic stabilizationReferences:
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