The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Ly...

We provide partial Lyapunov characterizations for a recently proposed generalization of input-to-state and integral input-to-state stability (ISS and iISS, respectively). This generalization relies on the notion of stability with respect to two measures originally introduced by Movchan [1960]. We show that the two classical Lyapunov characterizations of ISS-type properties, i.e., decrease condi...

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

This paper proposes new criteria for stability and performance of nonlinear interconnected systems by smoothly generalizing a recently-developed method of the state-dependent scaling. The criteria are directly related to Lyapunov functions so that they show how to construct Lyapunov functions which establish desired stability and performance explicitly. A set of popular Lyapunov stability crite...

This paper proposes a novel approach based on Lyapunov function method to analyse the stability of photovoltaic (PV) systems. The Lyapunov function is formulated using the method of quadratic forms, i.e., Krasovskii’s method. The stability of the photovoltaic systems under different operating conditions is analysed based on the formulated Lyapunov function. A comparison of stability analysis us...

The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. In this type of stability, trajectories converge to each other, rather than to an equilibrium point or a particular trajectory. Similarly to stability, Lyapunov functions play an important role in the study of incremental stability. In this paper, we propose coordinate-...