General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach

This paper is concerned with the problem of general output feedback stabilization for fractional order linear time-invariant (FO-LTI) systems with the fractional commensurate order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn>0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>α</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>2</mml:mn></mml:math>. The objective is to design suitable output feedback controllers that guarantee the stability of the resulting closed-loop systems. Based on the slack variable method and our previous stability criteria, some new results in the form of linear matrix inequality (LMI) are developed to the static and dynamic output feedback controllers synthesis for the FO-LTI system with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mn>0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>α</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>1</mml:mn></mml:math>. Furthermore, the results are extended to stabilize the FO-LTI systems with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>α</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>2</mml:mn></mml:math>. Finally, robust output feedback control is discussed. Numerical examples are given to illustrate the effectiveness of the proposed design methods.