In this paper, the problem of stability analysis is investigated for a particular class linear discrete time-delay systems .The criteria are derived by Lyapunov’s direct method using minimization with respect to a scalar parameter and they are expressed by norm and eigenvalue of appropriate matrices. The derived results present new delay independent stability conditions for linear discrete time...

|A nonholonomic motion planner for mobile manipulators moving in cluttered environments is presented. The approach is based on a discontinous feedback law under the infuence of a special potential eld. Convergence is shown via Lyapunov's direct method. Utilizing redundancy, the methodology allows the system to perform secondary, connguration dependent, objectives such as singularity avoidance. ...

This paper presents a novel stabilization result for the Furuta pendulum for a large region of attraction including almost all of the upper half plane. The solution is obtained via constructing a Lyapunov function after set of coordinate changes. Then, a set of differential equations are solved to achieve asymptotic stability which is proved in accordance with La Salle’s invariance principle. T...

The objective of this study was to get some sufficient conditions which guarantee the asymptotic stability and uniform boundedness of the null solution of some differential equations of third order with the variable delay. The most efficient tool for the study of the stability and boundedness of solutions of a given nonlinear differential equation is provided by Lyapunov theory. However the con...

In this paper, we use what we call the shift operator so that general delay dynamic equations of the form x (t) = a(t)x(t) + b(t)x(δ − (h, t))δ − (h, t), t ∈ [t0,∞)T can be analyzed with respect to stability and existence of solutions. By means of the shift operators we define a general delay function opening an avenue for the construction of Lyapunov functional on time scales. Thus, we use the...

To satisfy the performance specification and to have a good transient response of the system, the controlled system is often designed to possess a specific stability degree. If the controlled system has a stability degree  , we say that the system is exponentially stable. This paper gives sufficient condition for the exponential stability of linear discrete time delay systems. This new, delay-...

In this paper, by introducing the concept of command-to-state/output mapping, it is shown that the state of an uncertain nonlinear system can robustly be estimated if command-to-state mapping of the system and that of an uncertainty-free observer converge to each other. Then, a global Jacobian system is defined to capture this convergence property for the dynamics of estimation error, and a set...

The nonlinear stability of two populations diffusing in a common bounded domain with nonlinear density-dependent dispersal of a general type is studied, under Robin boundary conditions. The stability and instability of the positive equilibrium are studied by the linear eigenvalues method. The nonlinear stability is studied with the Lyapunov direct method. In a particular case, global stability ...

This paper addresses the problem of position control for robot manipulators. A new family of position controllers with gravity compensation for the global position of robots manipulators is presented. The previous results on the linear PD controller are extended to the new proposed family. The main contribution of this paper is to prove that the closed–loop system composed by full nonlinear rob...

Abstract:In this paper we study the hybrid projective synchronization and chaos control by using Adaptive feedback controllers based on Lyapunov's direct method Especially, the controller can be simplified into a single scalar one to achieve complete synchronization. Numerical simulations are demonstrated to verify the effectiveness of the control strategies