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Positive 1D and 2D Systems Book

Positive 1D and 2D Systems
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Positive 1D and 2D Systems, Moving on from earlier shastic and robust control paradigms, this book introduces the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. It significantly reduces the computational cost of high-quality cont, Positive 1D and 2D Systems
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  • Positive 1D and 2D Systems
  • Written by author Tadeusz Kaczorek
  • Published by Springer-Verlag New York, LLC, 4/30/2013
  • Moving on from earlier shastic and robust control paradigms, this book introduces the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. It significantly reduces the computational cost of high-quality cont
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Book Categories

Authors

1 Positive matrices and graphs 1
1.1 Generalised permutation matrix, nonnegative matrix, positive and strictly positive matrices 1
1.2 Reducible and irreducible matrices 3
1.3 The Collatz - Wielandt function 8
1.4 Maximum eigenvalue of a nonnegative matrix 10
1.5 Bounds on the maximal eigenvalue and eigenvector of a positive matrix 13
1.6 Dominating positive matrices of complex matrices 18
1.7 Oscillatory and primitive matrices 19
1.8 The canonical Frobenius form of a cyclic matrix 23
1.9 Metzler matrix 26
1.10 M-matrices 27
1.11 Totally nonnegative (positive) matrices 30
1.12 Graphs of positive systems 34
1.13 Graphs of reducible, irreducible, cyclic and primitive systems 41
2 Continuous-time and discrete-time positive systems 51
2.1 Externally positive systems 51
2.2 Internally positive systems 55
2.3 Compartmental systems 60
2.4 Stability of positive systems 63
2.5 Input-output stability 72
2.6 Weakly positive systems 79
2.7 Componentwise asymptotic stability and exponental stability of positive systems 97
2.8 Externally and internally positive singular systems 104
2.9 Composite positive linear systems 115
2.10 Eigenvalue assignment problem for positive linear systems 119
3 Reachability, controllability and observability of positive systems 127
3.1 Discrete-time systems 127
3.2 Continuous-time systems 136
3.3 Controllability of positive systems 139
3.4 Minimum energy control of positive systems 144
3.5 Reachability and controllability of weakly positive systems with state feedbacks 151
3.6 Observability of discrete-time positive systems 156
3.7 Reachability and controllability of weakly positive systems 161
4 Realisation problem of positive 1D systems 173
4.1 Basic notions and formulation of realisation problem 173
4.2 Existence and computation of positive realisations 175
4.3 Existence and computation of positive realisations of multi-input multi-output systems 201
4.4 Existence and computation of positive realisations of weakly positive multi-input multi-output systems 211
4.5 Positive realisations in canonical forms of singular linear 222
5 2D models of positive linear systems 241
5.1 Internally positive Roesser model 241
5.2 Externally positive Roesser model 243
5.3 Internally positive general model 248
5.4 Externally positive general model 250
5.5 Positive Fornasini-Marchesini models and relationships between models 251
5.6 Positive models of continuous-discrete systems 254
5.7 Positive generalised Roesser model 264
6 Controllability and minimum energy control of positive 2D systems 275
6.1 Reachability, controllability and observability of positive Roesser model 275
6.2 Reachability, controllability and observability of the positive general model 283
6.3 Minimum energy control of positive 2D systems 291
6.4 Reachability and minimum energy control of positive 2D continuous-discrete systems 297
7 Realisation problem for positive 2D systems 311
7.1 Formulation of realisation problem for positive Roesser model 311
7.2 Existence of positive realisations 312
7.3 Positive realisations in canonical form of the Roesser model 328
7.4 Determination of the positive Roesser model by the use of state variables diagram 332
7.5 Determination of a positive 2D general model for a given transfer matrix 337
7.6 Positive realisation problem for singular 2D Roesser model 340
7.7 Concluding remarks and open problems 359
App. A Determinantal Sylvester equality 367
App. B Computation of fundamental matrices of linear systems 387
App. C Solutions of 2D linear discrete models 403
App. D Transformations of matrices to their canonical forms and lemmas for 1D singular systems 411
Index 429


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Positive 1D and 2D Systems, Moving on from earlier shastic and robust control paradigms, this book introduces the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. It significantly reduces the computational cost of high-quality cont, Positive 1D and 2D Systems

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Positive 1D and 2D Systems, Moving on from earlier shastic and robust control paradigms, this book introduces the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. It significantly reduces the computational cost of high-quality cont, Positive 1D and 2D Systems

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Positive 1D and 2D Systems, Moving on from earlier shastic and robust control paradigms, this book introduces the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. It significantly reduces the computational cost of high-quality cont, Positive 1D and 2D Systems

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