Extremum properties of the two-dimensional linear time-varying (LTV) system are
used in this paper to estimate boundary of the attraction domain in the problem of the wheeled
robot control. To estimate the attraction domain of the nonlinear closed loop system, the Lyapunov function for the LTV system is constructed. A convex invariant function is known to exist at the boundary of the absolute stability region. For the second order case, the extremum trajectory, corresponding to the boundary of the absolute stability region, belongs to the level set of the invariant function. The periodic solution has finite number of switches on the period. It circumscribes the boundary of the attraction domain estimate. Two illustrative examples are considered.
