Nonlinear control of nonsquare multivariable systems

This paper is concerned with the synthesis of a nonlinear state feedback law for nonsquare multivariable nonlinear systems. Previous approaches in the literature have solved this problem by (1) squaring the system by discarding some inputs or by adding new outputs, or (2) by utilizing some inputs for input/output (I/O) linearization and the remaining inputs for minimizing cost. In this paper, a nonlinear feedback law is synthesized which utilizes all the available inputs to I/O linearize the system and minimize the cost of the control effort by solving a convex optimization problem on-line. This procedure is illustrated via simulation of a regulation problem in a nonlinear continuous stirred tank reactor with three inputs and two outputs.