Control design using Jordan controllable canonical form

In this paper, we present a new control design strategy for a class of single-input nonlinear dynamical systems. The design consists in transforming the system into a new controllable canonical form which we call the Jordan controllable canonical form (JCCF). In fact, the Brunowski controllable canonical form is an special case of the JCCF. We first show that any controllable pair can be transformed into the JCCF. We next, extend the result to a controllable pair which is state dependent. Using this extended Jordan controllable canonical form we propose a control design strategy for a class of single-input control affine systems. The design is simple and systematic and provides two degrees of freedom to fix the convergence of the closed-loop system. An example is given to illustrate the control design.