Fractional Linear Systems and Electrical Circuits (Studies in Systems, Decision and Control .13) (2015. 2014. xii, 254 S. 47 SW-Abb. 235 mm)

個数:

Fractional Linear Systems and Electrical Circuits (Studies in Systems, Decision and Control .13) (2015. 2014. xii, 254 S. 47 SW-Abb. 235 mm)

  • 在庫がございません。海外の書籍取次会社を通じて出版社等からお取り寄せいたします。
    通常6~9週間ほどで発送の見込みですが、商品によってはさらに時間がかかることもございます。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合がございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。

  • 提携先の海外書籍取次会社に在庫がございます。通常2週間で発送いたします。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 製本 Hardcover:ハードカバー版
  • 商品コード 9783319113609

Full Description


This monograph covers some selected problems of positive and fractional electrical circuits composed of resistors, coils, capacitors and voltage (current) sources. The book consists of 8 chapters, 4 appendices and a list of references. Chapter 1 is devoted to fractional standard and positive continuous-time and discrete-time linear systems without and with delays. In chapter 2 the standard and positive fractional electrical circuits are considered and the fractional electrical circuits in transient states are analyzed. Descriptor linear electrical circuits and their properties are investigated in chapter 3, while chapter 4 is devoted to the stability of fractional standard and positive linear electrical circuits. The reachability, observability and reconstructability of fractional positive electrical circuits and their decoupling zeros are analyzed in chapter 5. The fractional linear electrical circuits with feedbacks are considered in chapter 6. In chapter 7 solutions of minimum energy control for standard and fractional systems with and without bounded inputs is presented. In chapter 8 the fractional continuous-time 2D linear systems described by the Roesser type models are investigated.

Table of Contents

Preface                                            v
1 Fractional Differential Equations 1 (48)
1.1 Definition of Euler Gamma Function 1 (1)
and Its Properties
1.2 Mittag-Leffler Function 2 (1)
1.3 Definitions of Fractional 3 (3)
Derivative-Integral
1.3.1 Riemann-Liouville Definition 3 (2)
1.3.2 Caputo Definition 5 (1)
1.4 Solutions of the Fractional State 6 (5)
Equation of Continuous-Time Linear System
1.5 Positivity of the Fractional Systems 11 (1)
1.6 External Positivity of the Fractional 12 (1)
Systems
1.7 Positive Continuous-Time Linear 13 (2)
Systems with Delays
1.8 Positive Linear Systems Consisting of 15 (6)
N Subsystems with Different Fractional
Orders
1.8.1 Linear Differential Equations 15 (5)
with Different Fractional Orders
1.8.2 Positive Fractional Systems with 20 (1)
Different Fractional Orders
1.9 Descriptor Fractional Continuous-Time 21 (7)
Linear Systems
1.9.1 Solution of the Descriptor 22 (2)
Fractional Systems
1.9.2 Drazin Inverse Method for the 24 (4)
Solution of Fractional Descriptor
Continuous-Time Linear Systems
1.10 Definition of n-Order Difference 28 (2)
1.11 State Equations of the Discrete-Time 30 (1)
Fractional Linear Systems
1.11.1 Fractional Systems without Delays 30 (1)
1.11.2 Fractional Systems with Delays 31 (1)
1.12 Solution of the State Equations of 31 (7)
the Fractional Discrete-Time Linear System
1.12.1 Fractional Systems with Delays 31 (3)
1.12.2 Fractional Systems with Delays 34 (3)
in State Vector
1.12.3 Fractional Systems without Delays 37 (1)
1.13 Positive Fractional Linear Systems 38 (1)
1.14 Externally Positive Fractional 39 (2)
Systems
1.15 Fractional Different Orders 41 (3)
Discrete-Time Linear Systems
1.16 Positive Fractional Different Orders 44 (1)
Discrete-Time Linear Systems
1.17 Descriptor Fractional Discrete-Time 45 (4)
Linear Systems
1.17.1 Solution to the State Equation 45 (4)
2 Positive Fractional Electrical Circuits 49 (32)
2.1 Fractional Electrical Circuits 49 (3)
2.2 Positive Fractional Electrical 52 (21)
Circuits
2.2.1 Fractional R, C, E Type 53 (6)
Electrical Circuits
2.2.2 Fractional R, L, E Type 59 (5)
Electrical Circuits
2.2.3 Fractional R, L, C Type 64 (9)
Electrical Circuits
2.3 Analysis of the Fractional Electrical 73 (3)
Circuits in Transient States
2.4 Reciprocity Theorem for Fractional 76 (2)
Circuits
2.5 Equivalent Voltage Source Theorem and 78 (3)
Equivalent Current Source Theorem
3 Descriptor Linear Electrical Circuits and 81 (36)
Their Properties
3.1 Descriptor Linear Electrical Circuits 81 (16)
3.1.1 Regularity of Descriptor 84 (10)
Electrical Circuits
3.1.2 Pointwise Completeness of 94 (2)
Descriptor Electrical Circuits
3.1.3 Pointwise Degeneracy of 96 (1)
Descriptor Electrical Circuits
3.2 Descriptor Fractional Linear 97 (3)
Electrical Circuits
3.3 Polynomial Approach to Fractional 100(9)
Descriptor Electrical Circuits
3.4 Positive Descriptor Fractional 109(8)
Electrical Circuits
3.4.1 Pointwise Completeness and 114(3)
Pointwise Degeneracy of Positive
Fractional Descriptor Electrical
Circuits
4 Stability of Positive Standard Linear 117(14)
Electrical Circuits
4.1 Stability of Positive Electrical 117(1)
Circuits
4.2 Positive Unstable R, L, E Electrical 118(5)
Circuits
4.3 Positive Unstable G, C, is Electrical 123(3)
Circuit
4.4 Positive Unstable R, L, C, E Type 126(5)
Electrical Circuits
5 Reachability, Observability and 131(38)
Reconstructability of Fractional Positive
Electrical Circuits and Their Decoupling
Zeros
5.1 Decomposition of the Pairs (A, B) and 131(10)
(A, C) of Linear Circuits
5.2 Reachability of Positive Electrical 141(7)
Circuits
5.3 Observability of Positive Electrical 148(3)
Circuits
5.4 Constructability of Positive 151(4)
Electrical Circuits
5.5 Decomposition of the Positive Pair 155(2)
(A, B)
5.6 Decomposition of the Positive Pair 157(2)
(A, C)
5.7 Decoupling Zeros of the Positive 159(2)
Electrical Circuits
5.8 Reachability of Positive Fractional 161(6)
Electrical Circuits
5.9 Observability of Positive Fractional 167(2)
Electrical Circuits
6 Standard and Fractional Linear Circuits 169(28)
with Feedbacks
6.1 Linear Dependence on Time of State 169(10)
Variable in Standard Electrical Circuits
with State Feedbacks
6.2 Zeroing of the State Vector of 179(6)
Standard Circuits by State-Feedbacks
6.3 Zeroing of the State Vector of 185(4)
Standard Circuits by Output-Feedbacks
6.4 Zeroing of the State Vector of 189(8)
Fractional Electrical Circuits by
State-Feedbacks
7 Minimum Energy Control of Electrical 197(12)
Circuits
7.1 Minimum Energy Control of Positive 197(5)
Standard Electrical Circuits
7.2 Minimum Energy Control of Fractional 202(3)
Positive Electrical Circuits
7.3 Minimum Energy Control of Fractional 205(4)
Positive Electrical Circuits with Bounded
Inputs
8 Fractional 2D Linear Systems Described by 209(16)
the Standard and Descriptor Roesser Model
with Applications
8.1 Fractional Derivatives and Integrals 209(1)
of 2D Functions
8.2 Descriptor Fractional 2D Roesser 210(4)
Model and Its Solution
8.3 Fractional-Order Model of the Long 214(3)
Transmission Line
8.4 Standard Fractional 2D Roesser Model 217(4)
and Its Solution
8.5 Generalization of Cayley-Hamilton 221(4)
Theorem
A Laplace Transforms of Continuous-Time 225(10)
Functions and Z-Transforms of Discrete-Time
Functions
A.1 Convolutions of Continuous-Time and 225(1)
Discrete-Time Functions and Their
Transforms
A.2 Laplace Transforms of 226(3)
Derivative-Integrals
A.3 Laplace Transforms of Two-Dimensional 229(2)
Fractional Differintegrals
A.4 Z-Transforms of Discrete-Time 231(4)
Functions
B Elementary Operations on Matrices 235(2)
C Nilpotent Matrices 237(2)
D Drazin Inverse Matrix 239(4)
D.1 Definition and Properties of Drazin 239(1)
Inverse Matrix
D.2 Procedure for Computation of Drazin 240(3)
Inverse Matrices
Bibliography 243(10)
Index 253