Mahdi Sojoodi

Pouya Badri, Mahdi Sojoodi

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 linear matrix inequality based procedure of developing stabilizing output feedback control is preserved in spite of the complexity of assuming the most complete linear controller model, with direct feedthrough parameter. The proposed stability and stabilization theorems are applicable to FO-LTI systems with different fractional orders in one or both of and intervals. Eventually, some numerical examples are presented to confirm the obtained analytical results.

Pouya Badri, Mahdi Sojoodi

This paper addresses the problem of robust dynamic output stabilization of FO-LTI interval systems with the fractional order 0<α<2, 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 LMI-based 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. Keywords: Fractional-order system, interval uncertainty, linear matrix inequality (LMI), robust stabilization, dynamic output feedback.

Elyar Zavary, Mahdi Sojoodi

This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm design for low-order controller based on direct Lyapunov approach is proposed. In the presented algorithm the conditions containing the bilinear variables are decoupled into separate conditions without imposing equality constraints or considering an iterative search of the controller parameters. There is no any limiting constraint on the state space matrices and also we assumed the most complete output feedback controller. Simulations results are given to approve the effectiveness and the straightforwardness of the proposed design.