This paper discusses conditions on stability and stabilization of continuous T-S fuzzy systems. Stability analysis is derived via non-quadratic Lyapunov function technique and LMIs (Linear Matrix Inequalities) formulation to obtain an efficient solution. The nonquadratic Lyapunov function is built by inference of quadratic Lyapunov function of each local model. We show that stability condition ...

Keywords: Continuous time difference systems Exponential stability Lyapunov–Krasovskii functionals a b s t r a c t This paper provides further Lyapunov results for the exponential stability of linear continuous time difference system involving discrete and distributed delays. We consider such a class of systems in the case when the discrete and distributed delays are independent thus completing...

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in [19]. The second part provides sufficien...

Abstract: A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N -th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is ...

This paper presents an adaptive nonlinear position controller with velocity constraint, capable of combining the input-output linearization technique and Lyapunov stability theory. Based on the Lyapunov stability theory, the adaptation law of the proposed controller is derived along with the verification of the overall system’s stability. Computer simulation results demonstrate that the propose...

This paper studies stability and hybrid synchronization of a time-delay financial hyperchaotic system. Based on Lyapunov stability theorem and differential inequalities, stability is obtained by intermittent linear state feedback control. Furthermore, hybrid synchronization method is firstly proposed to synchronize a financial hyperchaotic system and globally synchronization is obtained by prop...

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

In this chapter, we propose to use a parametric multiplier approach to deriving parametric Lyapunov functions for robust stability analysis of linear systems involving uncertain parameters. This new approach generalizes the traditional multiplier approach used in the absolute stability literature where the multiplier is independent of the uncertain parameters. Our main result provides a general...

A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The gen...

Abstract We consider a nonlinear state transformation that allows us to work with non-quadratic polynomial Lyapunov functions. We use these polynomials to form Lyapunov functions to demonstrate simultaneous stability for a finite collection of linear systems. Under a weak definiteness condition, our main result, Theorem 3, shows that the minimum degree polynomial Lyapunov function that demonstr...