Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Abstract

We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0 < < 1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler's Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

“…19 It should be noted that similar conclusion is obtained when we compare our method in Theorem 2 with -independent methods in other works. [20][21][22][23][24][25][26][27] The similar procedure for stability test of system (47) for 1.5 < < 2 is performed and the result is depicted in Figure 4. It is noted that by -independent methods, [19][20][21][22][23][24][25][26][27]…”

“…According to this method, the stability of the integer-order system guarantees the stability of the main FOS. This method was extended for stability (check the works of Mahmoud et al 25 and Shao and Zuo 26 ) and observer-based control of the class of No-FOSs, 27 respectively. Similar to the stability analysis approaches based on Lyapunov's direct methods in other works, [19][20][21][22][23][24] the stability conditions of Mahmoud et al, 25 Shao and Zuo, 26 and Qiu and Ji 27 are only true for 0 < < 1 and they are independent of .…”

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

“…In order to stabilize FO linear time-invariant systems with interval uncertainties, Adelipour et al (2015) and Badri and Sojoodi (2019a) investigated the robust stability analysis and robust stabilization of the systems by introducing a new general state-space form and designing a robust dynamic output feedback controller, respectively. For the coefficient uncertainties, there are a lot of results for different research systems, such as FO linear systems with time-varying norm-bounded parameter or possible uncertainties (Chen et al (2019); Qiu and Ji (2017)), nonlinear FO uncertain systems with admissible time-variant uncertainty (Li (2018)), and uncertain nonlinear time-delay FO systems (Binazadeh and Yousefi (2018)). Besides, it is effective to add other control concepts to the robust stability analysis of systems.…”

Robust Performance and Observer Based Control for Periodic Discrete‐Time Uncertain Systems

“…In [13] a similar approach is used with the addition of a parametrization for the computation of the observer. In [14], an observer-based method is proposed for a class of nonlinear fractional-order uncertain systems with time-varying parameters. Finally, an LMI-based method is presented in [15] to compute periodic observer-based controllers capable of minimizing the H ∞ norm of the controlled system, in order to assure the desired robustness.…”