Improved Controller Design on Robust Approximate Feedback Linearization via LMI Approach

Feedback linearization has several extensions and approximate feedback linearization is one of actively studied areas. In [2], [4], a framework of approximate feedback linearization was established and a locally stabilizing controller was designed, respectively. In [3], the class of systems in parametric feedback form were considered and an adaptive controller was suggested. Then, this work has been intensively studied and extended by others. A recent work reported in [5] also deals with the systems in parametric feedback form. The approximately feedback linearized systems are also called a perturbed chains-of-integrators form in other literature [6]. In [6], a globally stabilizing controller was proposed under the triangularity condition with linear growth property. In [7], an adaptive controller was suggested under the feedforward condition. Therefore, it seems that most existing results have focused on a selective class of nonlinear systems by placing some structural conditions on the nonlinearities. Most recently, there was a robust controller design method in [1] where the explicit restrictions on nonlinearities are not required anymore. However, the method of [1] often leads to overly conservative design of controllers. In this letter, we propose a new design method which is improved over [1] such that it increases the flexibility of controller design and reduces the conservativeness. Also, the merits of [1] over other existing methods [2]–[7] are still retained.