The aim of this paper is to show that a real order generalization of the dissipative concepts is a useful tool to determine the stability (in the Lyapunov and in the input-output sense) and to design control strategies not only for fractional order non-linear systems, but also for systems composed of integer and fractional order subsystems (mixed-order systems). In particular, the fractional control of integer order system (e.g. PIλ control) can be formalized. The key point is that the gradations of dissipativeness, passivity and positive realness concepts are related among them. Passivating systems is used as a strategy to stabilize them, which is studied in the non-adaptive as well as in the adaptive case.

JO - Bulletin of the Polish Academy of Sciences: Technical Sciences L1 - http://www.journals.pan.pl/Content/112201/PDF/02_445-454_00744_Bpast.No.67-3_25.07.19_K3_TeX.pdf L2 - http://www.journals.pan.pl/Content/112201 IS - No. 3 EP - 454 KW - passivity KW - dissipativeness KW - adaptive KW - passivation KW - nonlinear mixed-order system KW - positive realness KW - control of nonlinear systems ER - A1 - Gallegos, J.A. A1 - Duarte-Mermoud, M.A. VL - 67 JF - Bulletin of the Polish Academy of Sciences: Technical Sciences SP - 445 T1 - On real order passivity UR - http://www.journals.pan.pl/dlibra/docmetadata?id=112201 DOI - 10.24425/bpasts.2019.128611