Input-to-state stability and positivity of non-homogeneous heat equation

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Nonnegative continuous-time linear systems

Input-to-state stability and positivity of non-homogeneous heat equation .

Conditions on positivity of a second order system

Table of contents :

Table of Contents
Notations
General Introduction
1 Theoretical framework 
1.1 Interval analysis
1.2 Nonnegative continuous-time linear systems
1.3 Interval observer for continuous-time linear systems
1.4 Interval observers for time-delay systems
1.5 Partial differential equations
2 Interval observer: approximation 
2.1 Approximation of distributed systems
2.2 Interval observer design
2.3 Control design
2.4 Example
3 PDE Interval observer 
3.1 Input-to-state stability and positivity of non-homogeneous heat equation
3.2 Interval observer design for the heat equation
3.3 Stabilizing control
3.4 Examples
4 Interval observer for second-order DDE 
4.1 Delay-independent positivity
4.2 Representation of the solution for delay differential equations
4.3 Conditions on positivity of a second order system
4.4 Problem statement
4.5 Interval observer design
4.6 Example
5 Conclusions 
Bibliography

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