Stabilization and practical asymptotic stability of abstract differential equations. (English) Zbl 1359.34060
Summary: This article studies the problem of stabilization of the infinite-dimension time-varying control systems in Hilbert spaces. We consider the problem of practical asymptotic stability with respect to a continuous functional for a class of abstract nonlinear infinite-dimensional processes with multivalued solutions on a metric space when the origin is not an equilibrium point. In the case of the existence of a differentiable Lyapunov functional, we obtain sufficient conditions for the practical stability of continuous semigroups in a Banach space.
MSC:
| 34H15 | Stabilization of solutions to ordinary differential equations |
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34D20 | Stability of solutions to ordinary differential equations |
| 47H20 | Semigroups of nonlinear operators |
Keywords:
abstract differential equations; controllability; Lyapunov functions; practical stability; Riccati equation; stabilizationReferences:
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