Asymptotic Controllability and Exponential Stabilization of Nonlinear Control Systems at Singular Points

L. Grüne: Asymptotic Controllability and Exponential Stabilization of Nonlinear Control Systems at Singular Points
SIAM Journal on Control and Optimization 36, 1585 - 1603, 1998

DOI: 10.1137/S0363012997315919
Keywords: stabilization of nonlinear system by feedback; nonlinear control systems; singular points; Lyapunov exponents; discounted optimal control problems; discrete feedback control; robustness of discrete feedback control; interrelation between controllability and stabilization; uniform exponential controllabiltiy; uniform exponential stabilizability; inverted pendulum
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Abstract:

We discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points. Using a discounted optimal control approach we construct discrete feedback laws minimizing the Lyapunov exponent of the linearization. Thus we obtain an equivalence result between uniform exponential controllability and uniform exponential stabilizability by means of a discrete feedback law.

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