This paper considers improving the tip regulation performance of a joint-PD controlled single-link flexible manipulator by introducing nonlinear strain feedback. The controller is developed by applying Lyapunov’s direct method. The stability of the closed-loop system is theoretically proven based on the partial differential equations (PDE’s) which govern the motion of the flexible robot, instea...

In this paper we consider the asymptotic stability of linear interval time-delay systems on the base of using Lyapunov’s direct method and methods of interval analysis. A sufficient condition of asymptotic stability is obtained using the concept of Lyapunov–Krasovsky functional.

A controller is developed for underactuated surface ships with only surge force and yaw moment available to globally track a reference trajectory generated by a suitable virtual ship in a frame attached to the ship body. The control development is based on Lyapunov’s direct method and backstepping technique, and utilizes several properties of ship dynamics and their interconnected structure. Nu...

Abstract: A method to design a boundary controller for global stabilization of threedimensional nonlinear dynamics of flexible marine risers is presented. Equations of motion of the risers are first developed in a vector form. The boundary controller at the top end of the risers is then designed based on Lyapunov’s direct method. It is shown that when there are no environmental disturbances, th...

This paper addresses the position control problem for robot manipulators. We present three new controllers with bounded actions supported by a rigorous stability analysis including the robot dynamics in the closed–loop using Lyapunov’s direct method and the LaSalle’s invariance principle. Besides the theoretical results, the performance of proposed controllers is illustrated by experimental res...

In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new method projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in A and A. The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the comp...

Stability of fractional-order nonlinear dynamic systems is studied using Lyapunov direct method with the introductions of Mittag–Leffler stability and generalized Mittag–Leffler stability notions. With the definitions of Mittag–Leffler stability and generalized Mittag–Leffler stability proposed, the decaying speed of the Lyapunov function can bemore generally characterized which include the exp...

In this paper, we consider global stability for a heroin model with two distributed delays. The basic reproduction number of the heroin spread is obtained, which completely determine the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyapunov function, we show that the drug use-free equilibrium is globally asymptotically stable if the basic reproduction number is l...

The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear statio...

Trailer systems consist of a steering tractor and a passive trailer linked together with rigid free joint. The backward driving of trailer system is more difficult than the forward driving, because the backward driving of trailer system is unstable. In this paper, we study the backward tracking control for trailer systems and implement the asymptotically stable tracking controller using Lyapuno...