In this paper we investigate the practical asymptotic and exponential partial stability of time-varying nonlinear systems. We derive some sufficient conditions that guarantee practical partial stability of perturbed systems using Lyapunov's theory where a converse theorem is presented. Therefore, we generalize some works which are already made in the literature. Furthermore, we present some illustrative examples to verify the effectiveness of the proposed methods.

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov functions are allowed to be indefinite. Then, under quite general assumptions, we first present a new converse stability theorem for a large class of time-varying systems which will be used to prove certain stability properties of nonlinear systems with perturbation. Therefore, a new Lyapunov function is presented that guarantees global asymptotic stability under some restrictions on the perturbed system. Furthermore, some illustrative examples are presented.

In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.

In this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.