Stability and stabilization analysis of fractional‐order linear time‐invariant (FO‐LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single‐order equivalent system for the given different‐order system is introduced by which a new stability condition is obtained that is easier to check in practice than the conditions known up to now. Then the stabilization problem of fractional‐order linear systems with different fractional orders via a dynamic output feedback controller with a predetermined order is investigated, utilizing the proposed stability criterion. The proposed stability and stabilization theorems are applicable to FO‐LTI systems with different fractional orders in one or both of 0 < α < 1 and 1 ≤ α < 2 intervals. Finally, some numerical examples are presented to confirm the obtained analytical results.

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This paper deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractionalorder linear time invariant (FO-LTI) systems by means of linear matrix inequalities (LMIs). Our purpose is to design a loworder controller that stabilizes the fractional-order linear system in the presence of model uncertainties. No limiting constraint on the state space matrices of the uncertain system is assumed in the design procedure. Furthermore, adopting the most complete model of linear controller, with direct feedthrough parameter, does not disturb the LMI-based approach of developing robust stabilizing control. Eventually, the authors illustrate the advantages of the proposed method by some examples and their numerical simulation.

This paper addresses the problem of robust dynamic output stabilization of FO-LTI interval systems with the fractional order < < , in terms of linear matrix inequalities (LMIs). Our purpose is to design a robust dynamic output feedback controller that asymptotically stabilizes interval fractional-order linear time-invariant (FO-LTI) systems. Sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. The LMIbased procedures of designing robust stabilizing controllers are preserved in spite of the complexity of assuming the most complete model of linear controller, with direct feedthrough parameter. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in the form of LMIs, which is more suitable to check due to various existing efficient convex optimization parsers and solvers. Finally, two numerical examples have shown the effectiveness of our results.

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This paper considers the problem of robust stability and stabilization for linear fractionalorder system with nonlinear uncertain parameters, with fractional order . A dynamic output feedback controller, with predetermined order, for asymptotically stabilizing such uncertain fractional-order systems is designed. The derived stabilization conditions are in LMI form. Simulation results of two numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems.

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