Descriptor Systems of Integer and Fractional Orders (Studies in Systems, Decision and Control, 367)

✍ Scribed by Tadeusz Kaczorek; Kamil Borawski

• Tongue: English
• Leaves: 264
• Category: Library

✦ Table of Contents

Preface
Acknowledgment
Contents
List of Symbols
1 Descriptor Linear Systems
1.1 Continuous-Time Systems
1.1.1 State Equations of Descriptor Continuous-Time Linear Systems
1.1.2 Solution to the State Equation of Descriptor Continuous-Time Linear Systems
1.1.3 Positive Descriptor Continuous-Time Linear Systems
1.1.4 Stability of Descriptor Continuous-Time Linear Systems
1.1.5 Superstability of Descriptor Continuous-Time Linear Systems
1.2 Discrete-Time Systems
1.2.1 State Equations of Descriptor Discrete-Time Linear Systems
1.2.2 Solution to the State Equation of Descriptor Continuous-Time Linear Systems
1.2.3 Positive Descriptor Discrete-Time Linear Systems
1.2.4 Stability of Descriptor Discrete-Time Linear Systems
1.2.5 Superstability of Descriptor Discrete-Time Linear Systems
1.3 Concluding Remarks
2 Fractional Descriptor Linear Systems
2.1 Continuous-Time Systems
2.1.1 Euler Gamma Function and Its Properties
2.1.2 Mittag-Leffler Function
2.1.3 Caputo Definition of Fractional Derivative-Integral
2.1.4 State Equations of Fractional Descriptor Continuous-Time Linear Systems
2.1.5 Solution to the State Equation of Fractional Descriptor Continuous-Time Linear Systems
2.1.6 Positive Fractional Descriptor Continuous-Time Linear Systems
2.1.7 Stability of Fractional Descriptor Continuous-Time Linear Systems
2.1.8 Superstability of Fractional Descriptor Continuous-Time Linear Systems
2.2 Discrete-Time Systems
2.2.1 Grünwald-Letnikov Fractional-Order Backward Difference
2.2.2 State Equations of Descriptor Discrete-Time Linear Systems
2.2.3 Solution to the State Equation of Fractional Descriptor Discrete-Time Linear Systems
2.2.4 Positive Fractional Descriptor Discrete-Time Linear Systems
2.2.5 Stability of Fractional Descriptor Discrete-Time Linear Systems
2.2.6 Superstability of Fractional Descriptor Discrete-Time Linear Systems
2.3 Concluding Remarks
3 Stability of Positive Descriptor Systems
3.1 Stability Tests for Positive Linear Systems
3.1.1 Continuous-Time Systems
3.1.2 Discrete-Time Systems
3.1.3 Fractional Continuous-Time Systems
3.1.4 Fractional Discrete-Time Systems
3.2 Stability of Positive Interval Systems
3.2.1 Continuous-Time Systems
3.2.2 Discrete-Time Systems
3.2.3 Fractional Continuous-Time Systems
3.2.4 Fractional Discrete-Time Systems
3.3 Stability of Nonlinear Systems with Positive Linear Parts
3.3.1 Continuous-Time Systems
3.3.2 Discrete-Time Systems
3.3.3 Fractional Continuous-Time Systems
3.3.4 Fractional Discrete-Time Systems
3.3.5 Analysis of Global Stability of Descriptor Continuous-Time Nonlinear Feedback Systems by the Use of Nyquist Plots
3.4 Concluding Remarks
Appendix A Extensions of the Cayley-Hamilton Theorem for Descriptor Linear Systems
A.1 Cayley-Hamilton Theorem for Descriptor Linear Systems with Commuting Matrices
A.2 Cayley-Hamilton Theorem for Descriptor Linear Systems with Noncommuting Matrices
A.3 Cayley-Hamilton Theorem for Drazin Inverse Matrices
Appendix B Computation of the Drazin Inverse
B.1 Method 1
B.2 Method 2
B.3 Method 3
Appendix C Laplace Transforms of Continuous-Time Functions and mathcalZ-Transforms of Discrete-Time Functions
C.1 Convolutions of Continuous-Time and Discrete-Time Functions and Their Transforms
C.2 Laplace Transforms of Derivative-Integrals
C.3 mathcalZ-Transforms of Discrete-Time Functions
Appendix D Nilpotent Matrices
Appendix References