Control design using Jordan controllable canonical form

Abstract

Presents a 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 a 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.