Ordinary Differential Equations

This book comprises a rigorous, self-contained treatment of initial-value problems for ordinary differential equations. It also includes an introduction to mathematical control theory as well as an introduction to the concept of input-to-state stability.

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature.

The following topics are particularly emphasised:

• existence, uniqueness and continuation of solutions,
• continuous dependence on initial data,
• flows,
• qualitative behaviour of solutions,
• limit sets,
• stability theory,
• invariance principles,
• introductory control theory,
• feedback and stabilization.

The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability.

Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

Provides a self-contained, rigorous and analytical treatment of initial-value problems for ordinary differential equations Includes an introduction to mathematical control theory which sets this text apart from others on the subject Allows for discontinuous time dependence in differential equations, but does not require Lebesgue integration theory Accessible to undergraduate students Includes supplementary material: sn.pub/extras

Autorentext

Hartmut Logemann is a Professor in the Department of Mathematical Sciences, University of Bath, UK. He has taught a large variety of topics, including courses in complex analysis, control theory, engineering mathematics, Lyapunov theory, ordinary differential equations and semigroups of linear operators. His research interests are in mathematical systems and control theory with emphasis on infinite-dimensional systems, nonlinearity, positivity and sampled-data control.

Eugene P. Ryan is Professor Emeritus in the Department of Mathematical Sciences, University of Bath, UK. He has lectured on a wide variety of topics to diverse audiences at both undergraduate and postgraduate levels, including courses on abstract analysis, control theory, nonsmooth optimization, ordinary differential equations, and mathematical methods for engineers & scientists. His research interests lie in mathematical systems and control theory, with emphasis on stabilization and optimization of nonlinear systems.

Inhalt
Introduction.- Linear differential equations.- Introduction to linear control theory.- Nonlinear differential equations.- Stability and asymptotic behaviour.- Stability of feedback systems and stabilization.