Stabilization of uncertain fractional order system with time‐varying delay using BMI approach

Abstract

This paper considers the systematic design of robust stabilizing state feedback controllers for fractional order nonlinear systems with time‐varying delay being possibly unbounded. By using the fractional Halanay inequality and the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of bilinear matrix inequalities are derived. The controllers can then be obtained by computing the gain matrices. In order to derive the gain matrices, two algorithms are proposed by using the existing computationally linear matrix inequality techniques. Two numerical examples with simulation results are provided to demonstrate the effectiveness of the obtained results.

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

“…Many real‐world systems can be modelled as system (1) with delay or without delay, which have been discussed in some existing papers, for examples, Refs. [10–12, 16–19, 56, 61] and so on.…”

Output-feedback-guaranteed cost control of fractional-order uncertain linear delayed systems

“…Remark 4 In Refs. (Chen et al 2017;He et al 2019;Huang et al 2019), a linear state feedback algorithm was employed to control FO delayed systems. Since output variables are easy to measure directly and have a clear physical meaning in most cases, the output feedback is easier to implement than the state feedback control.…”

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

“…Time delay causes instability, oscillation, and poor performance. Therefore, time-delayed systems have achieved a lot of attention in recent years (He et al, 2021). A lot of effective research has been presented dealing with the state estimation problem for nonlinear integer-order systems with time delay (Pourdehi and Karimaghaee, 2020; Sun et al, 2020).…”