Abstract
In this paper, the issue of stabilization for uncertain rectangular descriptor fractional order systems (FOS) with 0 <; α <; 1 is considered by designing dynamic compensators. Firstly, the uncertain rectangular descriptor FOS is reconstructed into an augmented uncertain square descriptor FOS. Due to introducing the augmented plant, dynamic compensator can equivalently be transformed into static output feedback. Secondly, two methods for the static output feedback controller design are provided. All results are expressed as a series of linear matrix inequalities (LMIs). Finally, three practical numerical examples are given to verify the effectiveness of the results proposed in this paper.
Highlights
Fractional calculus, proposed in Leibniz’s letter, is a generalization of integer-order to arbitrary-order calculus, which has a history of more than 300 years [1], [2]
In the view of the above observations, we study output feedback stabilization of uncertain rectangular descriptor fractional order systems with fractional order 0 < α < 1 in this paper
NORMALIZATION AND STABILIZATION OF AUGMENTED SYSTEM It is noticed that the augmented System (5) is a square descriptor fractional order systems (FOS)
Summary
Fractional calculus, proposed in Leibniz’s letter, is a generalization of integer-order to arbitrary-order calculus, which has a history of more than 300 years [1], [2]. Z. Zhao et al.: Output Feedback Stabilization of Uncertain Rectangular Descriptor FOS With 0 < α < 1 with rank constraints [31], [32], equality constraints [11], [33], [34], singular value decomposition of matrix [35]–[40]. In the view of the above observations, we study output feedback stabilization of uncertain rectangular descriptor fractional order systems with fractional order 0 < α < 1 in this paper. The remainder of this paper is organized as follows: Section 2 introduces some existing results and designs dynamic compensator which transform the rectangular descriptor FOS into square descriptor FOS.
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