Design of observers and feedback controllers using pseudo-linear models of nonlinear systems

This paper presents a new approach to design state observers and feedback controllers for nonlinear systems. The method requires neither the linearization of the system nor special state-space coordinate transformations. Instead, a nonlinear system is systematically decomposed into linear and nonlinear components. The nonlinear terms are then redefined as an auxiliary set of state variables and/or inputs. This leads to a pseudo-linear system representation that is mathematically equivalent to the original nonlinear system. The term pseudo-linear is used to differentiate between a truly linear system and one that is artificially constructed through the introduction of new variables. The advantage of this method is that equivalent pseudo-linear representations are easy to obtain. Even though the approach is akin to nonlinear state transformations, it is more flexible and allows one to construct much general models of nonlinear systems than direct nonlinear state transformations. The effectiveness of this approach is demonstrated by several examples.