Smooth memoryless time-varying control of a class of chained nonholonomic systems with input delays

In this paper, the control design for a class of chained nonholonomic systems, consisting of a linear subsystem and a bilinear chained subsystem with input delays, using smooth memoryless time-varying feedback will be investigated. For the linear subsystem, leveraging certain properties of parametric Lyapunov equations, a smooth, memoryless nonhomogeneous control law that guarantees exponential convergence is proposed. Then the bilinear chained subsystem is transformed into a linear time-varying system through a linear time-varying state transformation. By exploiting the structural properties of nonholonomic systems and applying the Razumikhin stability theorem, smooth linear memoryless time-varying controllers are designed. Both state feedback and observer-based output feedback are considered. Finally, the effectiveness of the proposed methods is demonstrated through a model for an underactuated axisymmetric spacecraft.