Abstract
This paper introduces a simple method of the design of the output feedback stabilizing controller (OFSC) for the nonlinear upper triangular fractional-order systems (NUTFOS). The OFSC which makes the closed-loop system asymptotically stable is given based on the fractional indirect Lyapunov method and the static gain control method. Furthermore, an algorithm is established to design OFSC for the NUTFOS. Finally, an example is presented to verify the validity of the proposed method.
Highlights
Fractional-order systems (FOS) have received a great deal of attention from mathematicians, physicists, chemists, biologists, and so on [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
The feedback control design problem is a hot topic for nonlinear fractional-order systems, such as linear matrix inequality (LMI) methods [15,16,17,18,19,20,21], adaptive backstepping control scheme [22,23,24], the static gain control method [25,26,27], etc
The static gain control method has been introduced to study the feedback control design problem of FOS especially fractional-order triangular systems; see [25,26,27]. Both the state feedback stabilizing controller (SFSC) and the output feedback stabilizing controller (OFSC) were designed for both lower triangular and upper triangular linear FOS in [25]
Summary
Fractional-order systems (FOS) have received a great deal of attention from mathematicians, physicists, chemists, biologists, and so on [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The static gain control method has been introduced to study the feedback control design problem of FOS especially fractional-order triangular systems; see [25,26,27]. Both the state feedback stabilizing controller (SFSC) and the OFSC were designed for both lower triangular and upper triangular linear FOS in [25]. Using the static gain control method and the fractional indirect Lyapunov method, design problems of both the SFSC and the OFSC for the nonlinear lower triangular FOS were investigated in [26].
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