A comparison between classical robust stability conditions

Abstract

The paper is focused on the comparison between some classical robust stability conditions for continuous-time linear time-invariant systems. Such conditions are given as lemmas in the paper, since their statements include some generalizations, needed in order to better compare (and use) them. The analysis is carried out by comparing pairwise the families of systems whose stabilization through a given compensator is guaranteed by each of the considered robust stability conditions. Some properties of the families are formally derived and stated, and some very simple examples are exhibited in order to illustrate the presented properties and comparisons. A theorem, representing an extension of one of the considered conditions, is proposed in order to overcome some difficulties arising in the use of the classical result

Design of controllers for hybrid linear systems with impulsive inputs and periodic jumps

“…In particular, given H(z), let Q(z) and G(z) be designed so that the closed loop system Σ D depicted in Figure 1 is asymptotically stable. Such a property can be easily verified, for example, by using the Nyquist criterion for multi-input multi-output systems [35][36][37]. and G(z) can be carried out by using directly the transfer function H(z), which, in turn, can be determined directly from the hybrid transfer function W ( , z) by using the expressions given in (10).…”

“…1 is asymptotically stable. Such a property can be easily verified, for example, by using the Nyquist criterion for multi‐input multi‐output systems [35–37].…”