Positive 1d And 2d Systems

1. Positive Matrices And Graphs.- 1.1 Generalised Permutation Matrix, Nonnegative Matrix, Positive And Strictly Positive Matrices.- 1.2 Reducible And Irreducible Matrices.- 1.3 The Collatz - Wielandt Function.- 1.4 Maximum Eigenvalue Of A Nonnegative Matrix.- 1.5 Bounds On The Maximal Eigenvalue And Eigenvector Of A Positive Matrix.- 1.6 Dominating Positive Matrices Of Complex Matrices.- 1.7 Oscillatory And Primitive Matrices.- 1.8 The Canonical Frobenius Form Of A Cyclic Matrix.- 1.9 Metzler Matrix.- 1.10 M-matrices.- 1.11 Totally Nonnegative (positive) Matrices.- 1.12 Graphs Of Positive Systems.- 1.13 Graphs Of Reducible, Irreducible, Cyclic And Primitive Systems.- Problems.- References.- 2. Continuous-ime And Discrete-ime Positive Systems.- 2.1 Externally Positive Systems.- 2.1.1 Continuous-time Systems.- 2.1.2 Discrete-time System.- 2.2 Internally Positive Systemst.- 2.2.1 Continuous-time Systems.- 2.2.2 Discrete-time Systems.- 2.3 Compartmental Systems.- 2.3.1 Continuous-time Systems.- 2.3.2 Discrete-time Systems.- 2.4 Stability Of Positive Systems.- 2.4.1 Asymptotic Stability Of Continuous-time Systems.- 2.4.2 Asymptotic Stability Of Discrete-time Systems.- 2.5 Input-output Stability.- 2.5.1 Bibo Stability Of Positive Continuous-time Systems.- 2.5.2 Bibo Stability Of Internally Positive Discrete-time Systems.- 2.6 Weakly Positive Systems.- 2.6.1 Weakly Positive Continuous-time Systems.- 2.6.2 Equivalent Standard Systems For Singular Systems.- 2.6.3 Reduction Of Weakly Positive Systems To Their Standard Forms.- 2.6.4 Weakly Positive Discrete-time Systems.- 2.6.5 Reduction Of Weakly Positive Systems To Standard Positive Systems.- 2.7 Componentwise Asymptotic Stability And Exponental Stability Of Positive Systems.- 2.7.1 Continuous-time Systems.- 2.7.2 Discrete-time Systems.- 2.8 Externally And Internally Positive Singular Systems.- 2.8.1 Continuous-time Systems.- 2.8.2 Discrete-time Systems.- 2.9 Composite Positive Linear Systems.- 2.9.1 Discrete-ime Systems.- 2