LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties

Abstract

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order [Formula: see text] is a known constant belonging to [Formula: see text]. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and stabilization problems.

Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

“…Possibly it includes external disturbances, unmodeled dynamics, parameter variations, or other factors that may be difficult to deal with. Therefore, compared with uncertain systems discussed in the existing literature , system denotes a more general class of systems.…”

“…There are some studies in control of FO uncertain systems with same order , but just a few touch the topic of uncertain multi‐order FO systems.…”

“…The second direction is based on the linear matrix inequality (LMI) approach, that is mainly applied to FO interval systems with uncertain parameters. The stabilization of FO interval systems with uncertain parameters by employing the LMI technique is addressed in .…”

“…The methods presented in attenuate or reject uncertainties by employing the high gains in the feedback‐loop of the SMC and the observer based feedback control. Besides those methods, another effective way is to estimate the uncertainty and to cancel its effects in the feedback‐loop.…”

Exact bounds for robust stability of output feedback controlled fractional‐order systems with single parameter perturbations

“…13 A fractional-order PI controller was provided for the closed-loop energy generation control in the work of Alagoz and Kaygusuz. 14 In addition, for servo system control, a fractional-order PID controller was proposed by using the multivariable multiobjective genetic algorithm in the work of Ren et al 15 Robust stability is a crucial issue in fractional-order control systems, 4,[16][17][18][19] because practical control systems are frequently affected by various types of perturbations and uncertainties such as interval uncertainties, 4,[20][21][22][23][24] norm bounded uncertainties, [25][26][27][28] polytopic uncertainties, 29 and structured uncertainties. [30][31][32] Some valuable research results on the robust stability of FOSs with different kinds of uncertainties were put forward in time domain.…”