k-Exponential stability of nonlinear delay systems

In this paper we introduce a new concept ofk-exponential stability.The k-exponential stability of nonlinear delay systems is studiedvia the nonlinear variation-of-parameters formula and nonlinearinequality analysis.     

On Nonlinear Perturbations of Nonlinear Dynamical Systems, and Applications to Control

The nonlinear variation-of-constants formula is generalizedto infinite-dimensional systems and applied to the stabilityproblem and used to obtain bounds on the states of a nonlinearcontrol system when the controls are bounded. The theory isillustrated by a simple model from nuclear reactor dynamics.     

Thermal Explosion with Variable Thermal Conductivity: Criticality and Its Disappearance

Thermal stability of reacting masses, whose thermal conductivityis a function of temperature, is investigated. Some generalresults relating to criticality and its disappearance are presented.A particular study is made of the disappearance of criticalityfor the slab geometry with infinite Biot number (Frank-Kamenetskiiconditions) for both linear and exponential forms for the temperaturedependence of conductivity.     

Optimal control and stabilization for nonlinear systems

The optimal control and stabilization of nonlinear systems ofthe form = A(x)x + B(x)u is considered andexplicit expressions for the control are developed. Excellentresults have been obtained when we apply the technique presentedhere to an anaytical nonlinear model of the F-8 fighter aircraft.     

Nonlinear Input-Output Maps For Bilinear Systems and Stability

The aim of this paper is to introduce two nonlinear input-outputrepresentations of bilinear systems. Sufficient conditions fora kind of L stability are derived. These representations arebelieved to compare favourably with the standard Volterra seriesrepresentation.     

On the Solution of Fredholm Integral Equations of the First Kind in L2

A method of solving numerically an integral equation of thefirst kind in L² is given and precise conditions are given forthe validity of the method. The method should be useful in physicalproblems where the kernel is calculated numerically and is notgiven as a known function.