Logemann, Hartmut.
Ordinary Differential Equations Analysis, Qualitative Theory and Control / [electronic resource] : by Hartmut Logemann, Eugene P. Ryan. - XIII, 333 p. 40 illus. online resource. - Springer Undergraduate Mathematics Series, 1615-2085 . - Springer Undergraduate Mathematics Series, .
Introduction -- Linear differential equations -- Introduction to linear control theory -- Nonlinear differential equations -- Stability and asymptotic behaviour -- Stability of feedback systems and stabilization.
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 students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.
9781447163985
10.1007/978-1-4471-6398-5 doi
Mathematics.
Differential equations.
System theory.
Vibration.
Dynamical systems.
Dynamics.
Mathematics.
Ordinary Differential Equations.
Systems Theory, Control.
Vibration, Dynamical Systems, Control.
QA372
515.352
Ordinary Differential Equations Analysis, Qualitative Theory and Control / [electronic resource] : by Hartmut Logemann, Eugene P. Ryan. - XIII, 333 p. 40 illus. online resource. - Springer Undergraduate Mathematics Series, 1615-2085 . - Springer Undergraduate Mathematics Series, .
Introduction -- Linear differential equations -- Introduction to linear control theory -- Nonlinear differential equations -- Stability and asymptotic behaviour -- Stability of feedback systems and stabilization.
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 students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.
9781447163985
10.1007/978-1-4471-6398-5 doi
Mathematics.
Differential equations.
System theory.
Vibration.
Dynamical systems.
Dynamics.
Mathematics.
Ordinary Differential Equations.
Systems Theory, Control.
Vibration, Dynamical Systems, Control.
QA372
515.352