State Space Consistency and Differentiability

By investigating the properties of the natural state, this book presents an analysis of input-output systems with regard to the mathematical concept of state. The state of a system condenses the effects of past inputs to the system in a useful manner. This monograph emphasizes two main properties of the natural state; the first has to do with the possibility of determining the input-output system from its natural state set and the second deals with differentiability properties involving the natural state inherited from the input-output system, including differentiability of the natural state and natural state trajectories. The results presented in this title aid in modeling physical systems since system identification from a state set holds in most models. Researchers and engineers working in electrical, aerospace, mechanical, and chemical fields along with applied mathematicians working in systems or differential equations will find this title useful due to its rigorous mathematics.

List of contents

1. Introduction.- 2. Preliminaries.- 3. Some state space properties.- 4. State differentiability properties in input-output systems.- 5. Summary and conclusion.

Summary

By investigating the properties of the natural state, this book presents an analysis of input-output systems with regard to the mathematical concept of state. The state of a system condenses the effects of past inputs to the system in a useful manner. This monograph emphasizes two main properties of the natural state; the first has to do with the possibility of determining the input-output system from its natural state set and the second deals with differentiability properties involving the natural state inherited from the input-output system, including differentiability of the natural state and natural state trajectories. The results presented in this title aid in modeling physical systems since system identification from a state set holds in most models. Researchers and engineers working in electrical, aerospace, mechanical, and chemical fields along with applied mathematicians working in systems or differential equations will find this title useful due to its rigorous mathematics. 

Product details

• Authors: Demetrios Serakos
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2015
• EAN: 9783319144689
• ISBN: 978-3-31-914468-9
• No. of pages: 72
• Dimensions: 155 mm x 4 mm x 235 mm
• Weight: 143 g
• Illustrations: XI, 72 p.
• Series: SpringerBriefs in Optimization; SpringerBriefs in Optimization
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Analysis, Algebra, C, Optimization, Civil Engineering, Mathematics and Statistics, Complex systems, Functional Analysis, Theoretical and Applied Mechanics, Ordinary Differential Equations, Mechanics, Mechanics of solids, Mechanics, Applied, Differential calculus & equations, Differential equations, Dynamical systems, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, Functional analysis & transforms, Field Theory and Polynomials, Field theory (Physics), Dynamics & statics, Statistical physics