Contents 1. INTRODUCTION
Stability is the most important characteristic in the system analysis and design. Many researcher have studied in this area [1]–[8]. A. Lyapunov [1] have proposed two methods for stability analysis. The Lyapunov's direct method is a sufficient condition and determining the Lyapunov function is the main problem in this method. K. Xiong [2] has studied the global asymptotic stability of a class of nonlinear dynamical systems based on the Lyapunov method. He obtained necessary and sufficient conditions for the existence of a Lyapunov function for a Lurie type problem with negative semi-definite derivative. He improved the Moore-Anderson's theorem and the Popov frequency criterion in this field. B. Xu [3] has established a necessary and sufficient conditions of generalized exponential stability for general retarded dynamic systems. W. M. Haddad et al. [4] developed several results on stability and dissipativity of discrete time linear and nonlinear nonnegative dynamical systems.
