Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback
This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The stability is defined with respect to a nonstandard dilation and is termed "δ-exponential" stability. The δ-exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm (1992) for smooth feedbacks. Converse Lyapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms.
© 1994 IEEE. Supported in part by AFOSR F49620-92J-0293. Supported in part by a grant from the Powell Foundation.
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