On the Practical Output Feedback Stabilization for Nonlinear Uncertain Systems

The problem of stabilization for uncertain systems has been widely investigated for many years [1–11]. In these studies, the origin was not supposed to be an equilibrium point of the uncertain system. So we can no longer expect to design a controller that guarantee the stability of the origin as an equilibrium point. In [1], a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state. [5], [9] and [6] presented controllers that guarantee exponential stability of a ball containing the origin of the state space and the radius of this ball can be made arbitrary small. In order to study uncertain dynamical systems, the authors in [12] introduced the notion of input to state practical stability. In [13], the concept of input to state practical stability is extended to stochastic case and an output feedback controller is proposed for a class of stochastic nonlinear systems with uncertain nonlinear functions. Most of the recent nonlinear controllers are designed for an uncertain system that has a nominal linear part and the controller is designed based on the knowledge of the upper bound, possibly time varying and state dependent, of the uncertainties vector norm. Another class of uncertain systems which has also received considerable attention, namely systems with nominal part which is affine in the control. Such a class of systems is important because it may represent many physical systems. In [2,8,10] authors investigated the state feedback stabilization problem for these systems. In this paper, we will synthesis an output feedback controller for this class of systems. It should be noted that output feedback stabilization problem for uncertain system with linear nominal part has been