Fractional and nD systems: a continuous case

Proportional plus integral control of ladder circuits modeled in the form of two-dimensional (2D) systems

“…super-capacitors, see Kaczorek (2011) and the literature therein. Here it should be mentioned that "fractional" systems stability can be analyzed in the multidimensional (nD) framework leading to the efficient results, see Bachelier et al (2012).…”

Robust stability and stabilization of multi‐order fractional‐order systems with interval uncertainties: An LMI approach

“…As follows, there are three contributions of this paper: Firstly, the new LMI‐based sufficient conditions for stability and stabilization of nominal MOFOSs are derived. Compared with the existing results, 29,30 ours are suitable for robust analysis and controller design of incommensurate MOFOSs. Secondly, against interval uncertainties, the LMI‐based sufficient conditions for robust stability of MOFOSs are presented. Thirdly, by designing state feedback controllers, the LMI‐based sufficient conditions for robust stabilization of MOFOSs with interval uncertainties are presented. …”

“…Recently, some LMI‐based results about stability of MOFOSs have been presented. The LMI‐based sufficient conditions for stability and stabilization of incommensurate MOFOSs involving multi‐orders have been proposed by applying the nD systems approach 29 . And the LMI‐based conditions for stability and stabilization of commensurate MOFOSs have been presented by transforming such systems into the same‐order fractional‐order systems equivalently 30 …”

“…And by the generalized Nyquist theorem, some robust stability conditions for MOFOSs with structured uncertainties or interval uncertainties have been presented, 36 but the results are also not suitable for controller design. For the existing LMI‐based results mentioned above, 29,30 it is difficult to solve the robust stability and stabilization problems of incommensurate MOFOSs.…”

Controllability Problem of Fractional Neutral Systems: A Survey

“…Many control systems arising from realistic models can be described as partial fractional differential or integrodifferential inclusions [33][34][35][36]. In [37] authors present a new approach to obtain the existence of mild solutions and controllability results.…”