DESIGN OF P AND PI STABILIZING CONTROLLERS FOR QUASI-LINEAR SYSTEMS

The systems studied in this paper are nonlinear systems perturbed by disturbances which are feedback transformable to quasi-linear systems [i.e. z̊ = Az + Bv + ζ(z)d with (A, B) controllable]. We consider the problem of designing stabilizing controllers for perturbed nonlinear systems through their equivalent quasi-linear systems. With the addition of integral action, we can guarantee not only ultimate δ-stabilization but also zero steady state offset for both the output of the quasi-linear system (y = Cz) and for the equivalent output [y = h(x)] of the nonlinear system. Moreover, when the so-called disturbance matching condition is satisfied, it is shown that all the states of the quasi-linear system (and the nonlinear system) will exhibit zero steady state offset. All the results presented here are for single control input systems. © 1990.