Finite-Time Stability and Stabilization of Fractional Order Positive Switched Systems

Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

“…This description of FTS is different from the one in [23], but they are the same definitions in nature.…”

“…Lemma 5 (see [23]). System (5) is positive if and only if , ∀ ∈ , are Metzler matrices and ∀ ∈ , ⪰ 0 and ⪰ 0.…”

“…Definition 2 (see [23]). System (5) is said to be positive if, for any switching signals ( ) and any initial conditions ( 0 ) ⪰ 0, the corresponding trajectory satisfies ( ) ⪰ 0 and ( ) ⪰ 0 for all ⪰ 0.…”

“…Peter [17] has firstly defined finite-time stability (FTS) for linear deterministic systems, which means that, given a bound on the initial condition, the system state does not exceed a certain threshold during a specified time interval. There have been some meaningful results about FTS of positive switched systems [18][19][20][21][22][23]. Among these results, it should be pointed out that only one paper has considered the problem of FTS of FOPSS in [23].…”

“…There have been some meaningful results about FTS of positive switched systems [18][19][20][21][22][23]. Among these results, it should be pointed out that only one paper has considered the problem of FTS of FOPSS in [23]. Moreover, when controlling a real plant, it is also desirable to design a control system which is not only finite-time stable but also guarantees an adequate level of performance.…”