Probabilistic robust stabilization of fractional order systems with interval uncertainty

Disturbance rejection FOPID controller design in v-domain

“…In this method, roots within the first Riemann sheet, which are called the principle characteristic roots [47] , are used for checking stability of the fractional order systems [14] , [15] , [16] , [17] , [18] , [20] , [46] , [47] . The conformal mapping maps stability region of complex -plane, which is the left half plane (LHP), to a slice of -plane that is confined by the angular range of .…”

“…System stability is an essential concern to be completed in for control system design tasks before consideration of controller performance concerns. For this reason, stabilization of non-integer order control systems has been deeply studied, and many works only addressed stability of such systems in several perspectives; stabilization of the systems according to system pole placements [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , closed loop system stabilization based on stability boundary locus (SBL) analyses [24] , stabilization by means of zero exclusion principle and value set analysis [25] , [26] . Linear Matrix Inequalities (LMI) technique was proposed for stability checking of fractional order systems [27] , [28] , [29] .…”

Robust stability analysis of fractional‐order interval systems with multiple time delays

“…10,11 Papers were published to introduce some criteria for the robust stability of fractional-order systems based on the concepts of value set, Young and Jensen inequalities, and principal characteristic equation. [12][13][14][15][16][17] Moreover, fractional-order controllers have been applied to control a diversity of dynamical processes, including both fractional-order and integer-order systems to increase the robustness. [18][19][20] On the other hand, modeling real world systems often includes some uncertainties.…”

“…Recently, using fractional‐order calculus for modeling physical systems widely has been spread because it can describe the behavior of many systems more accurately than its integer‐order counterpart, including delay systems . Papers were published to introduce some criteria for the robust stability of fractional‐order systems based on the concepts of value set, Young and Jensen inequalities, and principal characteristic equation . Moreover, fractional‐order controllers have been applied to control a diversity of dynamical processes, including both fractional‐order and integer‐order systems to increase the robustness .…”

Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

“…In the last decades, it has been frequently researched by many scientists to model real world problems. Therefore, it offered a decent way of implementation for plenty of models in miscellaneous areas of engineering and physics such as, electrical networks [9], fluid flow [11], image and signal processing [17], mathematical physics [30], viscoelasticity [25], biology [20], control [5] and see references therein [31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”