In this paper, the existence conditions of time-invariant asymptotic stabilizers and corresponding control laws for nonlinear driftless systems as given by x = g(x)u are presented. Based on Lyapunov stability criteria, sufficient and necessary conditions for the asymptotic stabilizability of driftless systems are obtained, specifically in terms of the orthogonality of the derivative of the Lyapunov function and the system dynamics. Sufficient conditions for system stabilization are also explicitly obtained by construction of both quadratic-type and integral-type Lyapunov functions. The corresponding stabilizing control laws are also presented. Moreover, the stabilizability conditions proposed in this paper are shown to cover the result obtained by Brockett in 1983.
|Number of pages||6|
|Journal||Journal of Control Systems and Technology|
|State||Published - 1 Sep 1996|