Systems with delays : analysis, control, and computations /
The main aim of the book is to present new constructive methods of delay differential equation (DDE) theory and to give readers practical tools for analysis, control design and simulating of linear systems with delays. Referred to as "systems with delays" in this volume, this class of diff...
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| Main Author: | |
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| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken, New Jersey :
John Wiley & Sons, Inc.,
[2015]
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| Subjects: | |
| Online Access: |
Full text (MFA users only) |
| ISBN: | 9781118998526 1118998529 9781118998540 1118998545 9781119117728 1119117720 9781119117841 1119117844 1119117585 9781119117582 9781119117735 1119117739 |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- Cover; Title Page; Copyright Page; Contents; Preface; 1 Linear time-delay systems; 1.1 Introduction; 1.1.1 Linear systems with delays; 1.1.2 Wind tunnel model; 1.1.3 Combustion stability in liquid propellant rocket motors; 1.2 Conditional representation of differential equations; 1.2.1 Conditional representation of ODE and PDE; 1.2.2 Conditional representation of DDE; 1.3 Initial Value Problem. Notion of solution; 1.3.1 Initial conditions (initial state); 1.3.2 Notion of a solution; 1.4 Functional spaces; 1.4.1 Space C[-{u01AC},0]; 1.4.2 Space Q[-{u01AC},0]; 1.4.3 Space Q[-{u01AC},0)
- 1.4.4 Space H = R{u019E} {u00D7} Q[-{u01AC},0)1.5 Phase space H. State of time-delay system; 1.6 Solution representation; 1.6.1 Time-varying systems with delays; 1.6.2 Time-invariant systems with delays; 1.7 Characteristic equation and solution expansion into a series; 1.7.1 Characteristic equation and eigenvalues; 1.7.2 Expansion of solution into a series on elementary solutions; 2 Stability theory; 2.1 Introduction; 2.1.1 Statement of the stability problem; 2.1.2 Eigenvalues criteria of asymptotic stability; 2.1.3 Stability via the fundamental matrix; 2.1.4 Stability with respect to a class of functions.
- 2.5.1 Linear system with discrete delay2.5.2 Linear system with distributed delays; 3 Linear quadratic control; 3.1 Introduction; 3.2 Statement of the problem; 3.3 Explicit solutions of generalized Riccati equations; 3.3.1 Variant 1; 3.3.2 Variant 2; 3.3.3 Variant 3; 3.4 Solution of Exponential Matrix Equation; 3.4.1 Stationary solution method; 3.4.2 Gradient methods; 3.5 Design procedure; 3.5.1 Variants 1 and 2; 3.5.2 Variant 3; 3.6 Design case studies; 3.6.1 Example 1; 3.6.2 Example 2; 3.6.3 Example 3; 3.6.4 Example 4; 3.6.5 Example 5: Wind tunnel model.
- 3.6.6 Example 6: Combustion stability in liquid propellant rocket motors4 Numerical methods; 4.1 Introduction; 4.2 Elementary one-step methods; 4.2.1 Euler'smethod; 4.2.2 Implicit methods (extrapolation); 4.2.3 Improved Euler'smethod; 4.2.4 Runge-Kutta-like methods; 4.3 Interpolation and extrapolation of the model pre-history; 4.3.1 Interpolational operators; 4.3.2 Extrapolational operators; 4.3.3 Interpolation-Extrapolation operator; 4.4 Explicit Runge-Kutta-like methods; 4.5 Approximation orders of ERK-like methods; 4.6 Automatic step size control; 4.6.1 Richardson extrapolation.