Linear controllers for tracking chained-form systems

In this paper we study the tracking problem for the class of nonholonomic systems in chained-form. In particular, with the first and the last state component of the chained-form as measurable output signals, we suggest a solution for the tracking problem using output feedback by combining a time-varying state feedback controller with an observer for the chained-form system. For the stability analysis of the "certainty equivalence type" of controller we use a cascaded systems approach. The resulting closed loop system is globally K-exponentially stable

Homogeneous Approximation, Recursive Observer Design, and Output Feedback

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The second tool is a new recursive observer design procedure for a chain of integrator. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems