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A New Class of Stabilizing State Feedback Controllers for Uncertain Nonlinear Dynamical Systems
state feedback controller synthesis
uniform ultimate boundedness
uniform asymptotic stability
nonlinear dynamical systems
The paper is mainly concerned with the problem of robust stabilization for a class of uncertain nonlinear dynamical systems. Based on the stabilizability of the nominal system (i. e. the system in the absence of uncertainty), a class of stabilizing state feedback controllers for this class of uncertain nonlinear dynamical systems are proposed. There exists a given feedback gain function in the state feedback controllers proposed in this paper. By appropriately choosing this gain function, the uniform ultimate boundedness and uniform asymptotic stability of uncertain nonlinear dynamical systems can respectively be guaranteed. In addition, the state feedback controllers proposed here are continuous, and with a rather simpler form than those reported in the literature. Therefore, the state feedback controllers developed by our approach can easily be implemented in some practical problems of robust stabilization for uncertain nonlinear dynamical systems. In this paper, we first discuss the problem of state feedback synthesis for uncertain nonlinear dynamical systems. Then, as a special case, we investigate the robust control problem of the uncertain dynamical systems whose nominal part is linear. Finally, several numerical examples are given to demonstrate the utilization of the approach developed in this paper. It is shown from the simulation results of these examples that by using the state feedback controller developed in this paper, the resulting closed-loop dynamical systems have rather good transient behavior, and no chattering will appear in implementation for the control.
広島大学総合科学部紀要. IV, 理系編