Smooth Memoryless Time-Varying Control of a Class of Chained Nonholonomic Systems with Input Delays

This paper investigates the smooth, memoryless, time-varying control design for a class of chained nonholonomic systems, comprising a linear subsystem and a bilinear chained subsystem with input delays. For the linear subsystem, a smooth, memoryless, nonhomogeneous control law is proposed by leveraging certain properties of parametric Lyapunov equations, ensuring exponential convergence. The bilinear chained subsystem is then transformed into a linear time-varying system via a linear time-varying state transformation. By exploiting the structural properties of nonholonomic systems and employing the Razumikhin stability theorem, a smooth, linear, memoryless, time-varying controller is developed. The effectiveness of the proposed methods is demonstrated using a model of an underactuated axisymmetric spacecraft.