Explicit Stability Conditions for Continuous Systems: A Functional Analytic Approach

by Michael I. Gil

Overview

Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.

Product Details

ISBN-13:	9783540239840
Publisher:	Springer Berlin Heidelberg
Publication date:	04/29/2005
Series:	Lecture Notes in Control and Information Sciences , #314
Edition description:	2005
Pages:	190
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Preliminaries.- Perturbations of Linear Systems.- Linear Systems with Slowly Varying Coefficients.- Linear Dissipative and Piecewise Constant Systems.- Nonlinear Systems with Autonomous Linear Parts.- The Aizerman Problem.- Nonlinear Systems with Time-Variant Linear Parts.- Essentially Nonlinear Systems.- The Lur'e Type Systems.- The Aizerman Type Problem for Nonautonomous Systems.- Input - State Stability.- Orbital Stability and Forced Oscillations.- Positive and Nontrivial Steady States.