Dynamic robust stabilization of fractional-order linear systems with nonlinear uncertain parameters: an LMI approach

Abstract

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.

Consensus of a class of nonlinear fractional-order multi-agent systems via dynamic output feedback controller

“…In continuous time systems without a delay, using quadratic functions as Lyapunov candidate is common. Desirable results of using quadratic functions as a Lyapunov candidate can be found in literature (Amini et al, 2016; Badri et al, 2021; Tartaglione et al, 2021). According to the literature, we selected the quadratic function (40) and got good and non-conservative results which is discussed in the simulation section.…”

“…In state feedback control scheme, all individual states of the system are needed to be measured and used in feedback line. However, in some practical situations, measuring all states is impossible or may sound difficult due to economic issues or physical limitations (Badri et al, 2021). In these cases, using output feedback control could be effective since there is no need to measure all individual states of the system and only by measuring outputs of the system, the control action is done.…”

“…In this paper, Gru¨nwald-Letnikov method is used to approximate the fractional derivatives. Gru¨nwald-Letnikov method is another approach which is widely used in different research areas to approximate fractional-order derivative, and for numerical methods, implementation is very effective (Badri et al, 2021;Shahamatkhah and Tabatabaei, 2020). As a result, we have used Gru¨nwald-Letnikov approximation approach for numerical solutions in this paper.…”