A class of non-linear fractional-order system stabilisation via fixed-order dynamic output feedback controller

TL;DR

This paper presents a systematic method for stabilizing a class of fractional-order nonlinear systems using fixed-order dynamic output feedback controllers, employing LMIs and a direct Lyapunov approach for low-order controller design.

Contribution

It introduces a new stabilisation algorithm that decouples bilinear variables in LMIs without iterative searches or constraints on state matrices.

Findings

Effective stabilization demonstrated through simulations

Decoupled conditions simplify controller design

No restrictions on state space matrices

Abstract

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.