Positive observer design for fractional order systems

Abstract

This paper initially starts with an overview of fractional order representation of linear continuous-time systems and their stability analysis. The design of fractional order observers for fractional order system (FOS) is considered with the purpose of estimating the system states in feedback implementation. Using the stability conditions for FOS, design procedures for both fractional order observer of proportional and proportional integral types (P <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> -Observer and PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> -Observer) are given with the aim of generalizing the conventional P- and PI-Observers. Finally, the problem of positive P <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> -Observer design for positive FOS is formulated and solved using linear programming. The possibility of incorporating P <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> -Observer and state feedback control law is also addressed for stabilization of FOS.