In this letter, we consider the global exponential stabilization problem by output feedback for a class of nonlinear systems. Along with a newly proposed matrix inequality condition, the proposed control method has improved flexibility in dealing with nonlinearity, over the existing methods. Analysis and examples are given to illustrate the improved features of our control method.

Since the control input of a feedback linearizable system depends on the diffeomorphism, the transient behavior of the controlled system is different. In this paper, we propose a switching rule for selecting a diffeomorphism so that the transient behavior is improved and the switched system is stable. Specifically, we show the sufficient condition for the exponential stability and the exponential upper bound of the trajectory of the switched system.