In this paper, the exponential stability of singularly perturbed discrete systems (SPDSs) with time-delay is investigated via the Lyapunov’s direct method. In the previous results about the SPDS with time-delay, the asymptotic stability is obtained using the frequency-domain approach. However, we propose a composite Lyapunov function to show that the SPDS with time-delay is exponentially stable...

In [6], Lyapunov’s direct method was used as a In practical applications of self-synchronizing chaotic systems, it is undesirable to be restricted to the wellknown low-dimensional systems; we need the ability to choose from a wide variety of high-dimensional chaotic systems. This paper discusses systematic synthesis procedures for achieving this capability. The significance of this work lies in...

In this article, we test a new control algorithm with non–linear structure for the position control problem of robot manipulators. We have demonstrated by taking into account the full nonlinear and multivariable nature of the robot dynamics, that the overall closed–loop system is globally asymptotically stable through the Lyapunov’s direct method together with LaSalle invariance principle. Expe...

This paper describes the use of direct method based on energy function type Lyapunov to evaluate the Critical Clearing Time (CCT) of power system subjected to large contingencies. The two axes model of generator with speed and excitation regulation systems is considered in this study. The power system model takes in consideration the presence of a Unified Power Flow Controller (UPFC). An energy...

In this paper we present a stabilization procedure for PVTOL (planar vertical take off and landing) aircraft with zero coupling coefficient that is defined as the effect of rolling moment on lateral acceleration. A stabilizing control structure has been designed via Lyapunov’s direct method including almost the whole state space and its asymptotic convergence has been proven using La Salle’s in...

non-fragile observer design is the main problem of this paper. using continuous frequency distribution, the stability conditions based on integer order lyapunov theorem are derived for lipschitz class of nonlinear fractional order systems. the proposed observer is stable beside the existence of both gain perturbation and input disturbance. for the first time, in this paper a systematic method i...

We develop a model for second order statistics of turbulent channel flow using an associated linear stochastically forced input-output system. The correlation operator of the velocity fields is computed by solving the appropriate Lyapunov equations of a Galerkin approximation of the original system. We use a variety of excitation force correlations and show the dependence of the velocity fields...

This paper deals with the position control of robot manipulators. Proposed is a simple class of robot regulators consisting of a linear proportional–derivative (PD) feedback plus an integral action of a nonlinear function of position errors. By using Lyapunov’s direct method and LaSalle’s invariance principle, the authors characterize a class of such nonlinear functions, and they provide explic...

In this paper we address the problem of augmenting a linear observer with an adaptive element. The design of the adaptive element employs two nonlinearly parameterized neural networks, the input and output layer weights of which are adapted on line. The goal is to improve the performance of the linear observer when applied to a nonlinear system. The networks’ teaching signal is generated using ...

In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signa...