STATE OBSERVERS AND STATE-FEEDBACK CONTROLLERS FOR A CLASS OF NON-LINEAR SYSTEMS

A design methodology for observers and controllers for a class of single-input, single-output nonlinear systems is developed. A nonlinear observer form is defined, and a corresponding observer using nonlinear observer gains is specified. The resulting errors of dynamics, which are nonlinear, are asymptotically stable for a proper choice of those gains and bounded inputs and outputs. A nonlinear closed-loop dynamics with arbitrary eigenvalue placement is devised. Transformations from the class of interest to the defined forms are derived. In the observer case, the transformation to the observer form and the nonlinear entries in the state matrix of that form can be determined separately, leading to a system of linear partial-differential equations - a major simplification. In the controller case, a simple system of linear partial-differential equations is obtained. The efficacy of the developed methodology is shown by employing a nonlinear, third-order model of a vehicle's longitudinal dynamics in the design process. Both here, and in other simulations, the latter results in a considerable improvement over a linearization/classical-design approach - especially in situations where the nonlinear effects are pronounced. It has advantages over parameter scheduling, especially for systems where the nonlinearities are functions of many state variables, resulting in a large number of operating points.