Global asymptotical stability and global finite-time stability for nonlinear homogeneous systems

Abstract

AbstractIn this paper, we investigate global asymptotical stability and global finite-time stability for a class of nonlinear homogeneous systems with different degree of homogeneity which can be greater or less than 0, respectively. The results are obtained by the property of homogeneity and local behaviour near the origin. A key contribution of this paper is the best possible lower bound of degree of homogeneity. The results are also extended to a variation of the nonlinear homogeneous systems that are found to be useful in the design of nonlinear finite-time observers. A numerical example is given to show the validity of our main results.