Linear feedback stabilization of nonlinear systems with an uncontrollable critical mode. (English) Zbl 0782.93078
Summary: Linear feedback stabilization of nonlinear systems is studied for systems whose linearization at an equilibrium point possesses a simple critical mode that is uncontrollable. The results complement previous work on the synthesis of nonlinear stabilizing control laws. The present work addresses continuous-time systems for which the linearization has either a simple zero eigenvalue or a pair of simple pure imaginary eigenvalues. Both the stability analysis and stabilizing control design employ results on stability of bifurcations of parameterized systems.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
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