in this paper we use a class of stochastic functional kolmogorov-type model with jumps to describe the evolutions of population dynamics. by constructing a special lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

This paper develops Lyapunov functions for power systems which have dynamic reactive power loads. These functions are extensions of earlier Lyapunov functions derived for structure preserving power system models having static loads. In order to obtain strict Lyapunov functions, the transient response of the dynamic load must have a logarithmic dependence on voltage. A Lyapunov function is initi...

Motivated by the fact that delay difference inclusions (DDIs) form a rich modeling class that includes, for example, uncertain time-delay systems and certain types of networked control systems, this paper provides a comprehensive collection of Lyapunov methods for DDIs. Firstly, the Lyapunov-Krasovskii approach, which is an extension of the classical Lyapunov theory to time-delay systems, is co...

Stability analysis of polynomial differential equations is a central topic in nonlinear dynamics and control which in recent years has undergone major algorithmic developments due to advances in optimization theory. Notably, the last decade has seen a widespread interest in the use of sum of squares (sos) based semidefinite programs that can automatically find polynomial Lyapunov functions and ...

Let ẋ = f(x, u) be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s g...

finding a suitable estimation of stability domain around stable equilibrium points is an important issue in the study of nonlinear dynamical systems. this paper intends to apply a set of analytical-numerical methods to estimate the region of attraction for autonomous nonlinear systems. in mechanical and structural engineering, autonomous systems could be found in large deformation problems or c...

Robust stability analysis of uncertain discrete time systems is studied. The LMI robust stability analysis method based on polynomial parameter dependent Lyapunov function is presented. This method is compared with other robust stability analysis methods formulated through LMI using linear parameter dependent Lyapunov function. The results are tested on randomly generated examples.

In this paper, the notion of complete Lyapunov function of control systems is introduced. The purpose is to determine a continuous real-valued function that describes the global structure of the system. The existence of complete Lyapunov functions is proved for certain classes of affine control systems on compact manifolds. © 2011 Elsevier B.V. All rights reserved.

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...