Feedback Linearization of Nonlinear Multivariable Systems

In this paper, we explore feedback linearization for nonlinear multivariable systems, a sophisticated control methodology that transforms nonlinear systems into equivalent linear forms to facilitate controller design. The discussion covers fundamental concepts and mathematical principles, with particular emphasis on multi-input multi-output (MIMO) system applications. Implementation typically involves computing coordinate transformations using Lie derivatives and designing control laws that cancel nonlinearities through state feedback. We examine advantages such as exact linearization capability and disadvantages including sensitivity to model uncertainties, while comparing performance with alternative control strategies like sliding mode and adaptive control. Through MATLAB code examples demonstrating Jacobian calculations and feedback gain tuning, readers will gain practical insights into applying feedback linearization to address complex nonlinear control challenges in multivariable systems.