Exponential Stability of Nonlinear Non-autonomous Multivariable Systems
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2015, Vol 35, Issue 1
Abstract
We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady state. As a particular case we obtain absolute stability conditions. Our approach is based on a combined usage of the properties of the "frozen" Lyapunov equation, and recent norm estimates for matrix functions. An illustrative example is given.
Authors and Affiliations
Michael I. Gil'
Keywords
Related Articles
- EP ID EP468129
- DOI 10.7151/dmdico.1168
- Views 67
- Downloads 0
Exponential Stability of Nonlinear Non-autonomous Multivariable Systems
We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are form...
Preface
-
Necessary conditions of optimality for a class of stochastic differential equations on UMD Banach spaces
In this paper we consider stochastic evolution equations on UMD-Banach spaces. In a recent paper we proved existence of optimal controls. Here in this paper we develop necessary conditions of optimality whereby one can...
Boundedness of set-valued stochastic integrals
The paper deals with integrable boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrable bounded. The problem of in...
Stochastic nonlinear Schrödinger equation and its laser induced optimal feedback control
In this paper we consider a class of nonlinear stochastic Schrödinger equations and their optimal control through laser induced electro-magnetic field. These equations arise in the field of optics. We prove existence and...