this paper studies the consensus problem of nonlinear leader-following multi-agent systems (mas). to do this, the error dynamics between the leader agent and follower ones are described via a takagi-sugeno (ts) fuzzy model. if the obtained ts fuzzy model is stable, then all of the nonlinear agents reach consensus. the consensus problem is investigated based on the parameterized or fuzzy lyapuno...

In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions Vn in a rational functional form approximating a maximal Lyapunov function VM that can be used to find an estimation for the DOA. Based on this idea, an improved method has been deve...

The method of Lyapunov functions (Lyapunov's second or direct method) was originally developed for studying the stability of a xed point of an autonomous or non-autonomous diierential equation. It was then extended from xed points to sets, from diierential equations to dynamical systems and to stochastic diierential equations. We go one step further and develop Lyapunov's second method for rand...

The long time behavior of arbitrary order fully discrete approximations using the discon-tinuous Galerkin method (see Johnson J]) for the time discretization of a reaction{diiusion equation is studied. The existence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully discrete scheme has a Lyapunov functional.

The long time behavior of arbitrary order fully discrete approximations using the discon-tinuous Galerkin method (see Johnson J]) for the time discretization of a reaction{diiusion equation is studied. The existence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully discrete scheme has a Lyapunov functional.

A nonlinear chattering-free sliding mode control method is designed to stabilize fractional chaotic systems with model uncertainties and external disturbances. The main feature of this controller is rapid convergence to equilibrium point, minimize chattering and resistance against uncertainties. The frequency distributed model is used to prove the stability of the controlled system based on dir...

In a previous paper [6] we suggested a numerical method for computing all Lyapunov exponents of a dynamical system by spatial integration with respect to an ergodic measure. The method extended an earlier approach of Aston and Dellnitz [2] for the largest Lyapunov exponent by integrating the diagonal entries from the QR-decomposition of the Jacobian for an iterated map. In this paper we provide...

Abstract: This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discre...

A novel Lyapunov function, which contains a concept of transfer function, was constructed to prove the rightness of a new kind of robust backstepping filter derivative control method. Meanwhile, the relationship between Lyapunov function and transfer function was established, which is an important concept that can be applied in a large family of control systems. Also, the backstepping design te...

In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact set of a dynamical system: the method of characteristic exponents (estimates of KaplanYorke type) and the method of Lyapunov functions. In the first approach, using Lyapunov's first method we exploit charachteristic exponents for obtaining such estimate. A close relationship with uniform asymptot...