Ordinary Differential Equations

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 the 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 studentsof mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

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.