title: Robust stabilization of uncertain nonlinear slowly-varying systems: application in a time-varying inertia pendulum.
abstract: This paper considers the problem of robust stabilization of nonlinear slowly-varying systems, in the presence of model uncertainties and external disturbances. The main contribution of this paper is an extension of the Slowly-Varying Control Lyapunov Function (SVCLF) technique to design a robust stabilizing controller for nonlinear slowly-varying systems with matched uncertainties. In the proposed strategy, the Lyapunov redesign method is utilized to design a robust control law. This method, originally, leads to a discontinuous controller which suffers from chattering. In this paper, this problem is removed by using a saturation function with a high slope, as an approximation of the signum function. Since, using the saturation function leads to loss of asymptotic stability and, instead, guarantees only the boundedness of the system's states; therefore, some sufficient conditions are proposed to guarantee the asymptotic stability of the closed-loop uncertain nonlinear slowly-varying system (without chattering). Also, in order to show the applicability of the proposed method, it is applied to a time-varying inertia pendulum. The efficiency of the designed controller is demonstrated through analysis and simulations.
authors.affiliation: School of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, Shiraz, Iran. Electronic address: binazadeh@sutech.ac.ir.
authors.forename: T
authors.initials: T
authors.lastname: Binazadeh
authors.affiliation: School of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, Shiraz, Iran. Electronic address: shafiei@sutech.ac.ir.
authors.forename: M H
authors.initials: MH
authors.lastname: Shafiei
keywords: Boundedness; Nonlinear uncertain slowly-varying system; Robust stabilizing controller; Slowly-Varying Control Lyapunov Function (SVCLF)