Positive Control with Maximum Stability Radius for Continuous-time Dynamic Systems
نویسنده
چکیده
........................................................................................................................................................ 2 Acknowledgements ....................................................................................................................................... 3 Introduction .................................................................................................................................................. 6 Chapter 1 – Mathematical Background and Literature Review .................................................................... 9 Positive Matrices ........................................................................................................................... 9 1.1.1. Maximal Eigenvalue of a Nonnegative Matrix .................................................................... 11 1.1.2. Bounds on Maximal Eigenvalue of a Positive Matrix .......................................................... 13 Metzler Matrices ......................................................................................................................... 15 M-Matrices .................................................................................................................................. 16 Totally nonnegative (positive) matrices ...................................................................................... 19 Chapter 2 – Continuous-time Positive Systems .......................................................................................... 21 Externally Positive Systems ......................................................................................................... 21 Internally Positive Systems ......................................................................................................... 22 Chapter 3 – Stability of Positive Systems .................................................................................................... 28 Asymptotic Stability .................................................................................................................... 28 Bounded-Input Bounded-Output (BIBO) Stability ...................................................................... 30 Asymptotic Stability using Lyapunov Equation ........................................................................... 34 Robust Stability of Perturbed Systems ....................................................................................... 35 3.4.1. General Uncertain Systems ................................................................................................. 35 3.4.2. Uncertain Interval Systems ................................................................................................. 36 Stability Radius ............................................................................................................................ 37 3.5.1. Complex Stability Radius ..................................................................................................... 39 3.5.2. Real Stability Radius ............................................................................................................ 40 Chapter 4 – Positive Stabilization with Maximum Stability Radius ............................................................ 42 Positive (Metzlerian) Stabilization .............................................................................................. 42 Maximizing Stability Radius by State Feedback .......................................................................... 45 Chapter 5 – Positive Time Delay System Stabilization with Maximum Stability Radius ............................. 48 Positive (Metzlerian) Stabilization .............................................................................................. 48 5.1.1. Case 1 .................................................................................................................................. 50 5.1.2. Case 2 .................................................................................................................................. 52 Maximizing Stability Radius by State Feedback .......................................................................... 54
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