Michael I. Gil

Stability of Finite and Infinite Dimensional Systems

From the Publisher: The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first year graduate level course in analysis.

The Freezing Method for Linear Difference Equations

The freezing method for ordinary differential systems is extended to difference systems. By virtue of that method, new stability criteria and solution estimates for linear difference systems are derived.

Stability analysis of a rigid robot with output-based controller and time delay ☆

This study considers the problem of stabilizing a rigid robot with an output-based controller and time-delayed input functions applied to the robot joints. We establish sufficient conditions for asymptotic stability of the system under consideration. These conditions are based on well-defined relationships between the magnitude of the controller gains and the time delay factor.

Iterative regulation of an electrically driven flexible-joint robot with model uncertainty

Considers the set-point regulation control problem of rigid and flexible-joint electrically driven robots with model uncertainties and unknown payloads. The proposed control scheme is based on simple linear state and output feedbacks. The resulting controller can also be implemented in a case where the current signal is not measurable. Applications of the approach when the Coulomb friction forces are taken into account have also been considered.

Point-to-point regulation of a robot with flexible joints including electrical effects of actuator dynamics

This paper considers the set-point tracking problem in rigid and flexible-joint robots when both the mechanical as well as the electrical effects of the actuator dynamics are taken into account. The suggested controllers are based on state and output feedbacks. The current approach demonstrates that for every given desired operating point, linear state and output feedbacks with constant feedforwards can be constructed such that the closed-loop system is globally asymptotically stable.

On absolute stability of differential-delay systems

A nonlinear differential-delay system with many nonlinearities is studied. A new absolute stability criterion is derived. >

Perturbations of functions of diagonalizable matrices

Let A and ˜ A be n × n diagonalizable matrices and f be a function defined on their spectra. In the present paper, bounds for the norm of f(A) f( ˜ A) are established. Applications to differential equations are also discussed.

On invertibility and positive invertibility of matrices

Abstract New non-singularity and non-negative invertibility criteria for matrices are derived. They yield new bounds for the spectrum. Moreover, we obtain a bound for the norm of the inverse matrix and new estimates for the spectral radius.

Periodic solutions of a perturbed difference equation

Existence theorems are obtained for the periodic solutions of a perturbed difference equation xk+1 = Axk+Fk(xk), where is a T periodic sequence of continuous mappings. Estimates for the maximum norms of these solutions are also obtained

Stability of a time discrete perturbed dynamical system with delay

Let Cn be the set of n complex vectors endowed with a norm ‖⋅‖Cn. Let A,B be two complex n×n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type uk