Interval observers design for discrete-time linear switched systems

Interval observer design method for asynchronous switched systems

“…The direct LMI method in [17] requires that A i − L i C i , i = 1, 2, …, n are all Metzler (or non-negative), which is known as a strong conservative condition. While in [18][19][20][21][22], the method of coordinate transformation is utilised to make…”

“…As an alternative way, some researchers have focused on estimating the bounds of the state [15,16], which relates to the interval observer design. In recent years, the design methods of interval observers for switched systems have been studied intensively [17][18][19][20][21][22]. In [17], when the error systems satisfied the condition that A i − L i C i are both Metzler and Hurwitz, the interval observers were directly designed for continuous-time switched systems.…”

“…However, in most cases, it is impossible to obtain the suitable gains L i satisfying that A i − L i C i are Metzler (or non-negative). The authors in [18] used a transformation matrix P to overcome the mentioned drawback. While in [19], the framework of interval observers design was established via the time-varying transformation of coordinates.…”

“…Furthermore, the different time-invariant coordinate transformation P i and timevarying coordinate transformation P i (t) were introduced for corresponding subsystems in [20,21], respectively, which reduces the conservatism of the existing conditions of interval observers. On the basis of [18][19][20][21], the work [22] employed bounded-real lemma to get a more compact interval so that an optimal interval observer can be designed. However, as pointed out in [23], it is unable to determine the appropriate transformation matrices and observer gains simultaneously such that the cooperativity, as well as, the disturbance performance is guaranteed.…”

H∞ interval observer design for uncertain discrete-time linear switched systems with unknown inputs

“…Many of the dynamical systems encountered in practice are of hybrid nature. Recently, framers and interval observers design for switched systems which consist of a finite number of subsystems governed by switching signals have received a great interest [7], [8], [14], [15], [19]. Usually, it is not very difficult to achieve the framer property, which is the notion of providing intervals in which state variables stay, if one does not care about the length of estimated intervals (i.e., the stability property).…”