Singular systems of differential equations

0. Introduction......Page 10
2. Concepts and Notations of Matrix Theory......Page 13
3. The Index and the Drazin Inverse......Page 16
4. Functions of a Matrix......Page 18
5. Representation of Matrix Functions by Contour Integrals......Page 22
6. Delta Functions......Page 23
7. Exercises......Page 25
2. Control Problems......Page 27
3. Electrical Circuits and Impulsive Behavior......Page 32
4. The Leslie Population Growth Model......Page 33
5. The Leontief Model......Page 36
6. Singular Perturbations......Page 37
1. Square Coefficients......Page 41
2. Rectangular Coefficients......Page 49
3. Boundary Values......Page 54
4. Delay Equations......Page 58
5. Application to Control Problems......Page 65
6. Discrete Systems and Applications......Page 76
7. Exercises......Page 86
2. Expansion of 1/(sA + B)......Page 88
3. Application to Differential Equations......Page 91
1. Introduction......Page 95
2. exp((A + B/ε)t) ; Existence of Limit......Page 96
3. exp((A + B/ε)t) ; The Asymptotic Expansion......Page 104
4. exp((A + B/ε)t) ; Nonconstant A,B......Page 109
5. Additional Powers of ε; Existence of Limits......Page 111
6. Additional Powers of ε; the Full Expansion......Page 121
7. More General Autonomous Systems......Page 126
8. Some Applications......Page 137
9. Products of Exponentials......Page 144
1. Introduction......Page 147
2. Reduction to Constant Coefficients......Page 148
3. Reduction of A(dx/dt) + Bx = f  to A\'(dx/dt) + x =f\'......Page 151
4. A\' of Constant Rank - Reduction Methods......Page 154
5. Nonautonomous Discrete Systems......Page 160
7. Computation......Page 163
1. Background and Problems......Page 168
2. Second Order Systems......Page 172
REFERENCES......Page 176
INDEX......Page 181
LIST OF SYMBOLS......Page 184