Stability properties of a class of positive switched systems with rank one difference

作者：Fornasini Ettore; Valcher Maria Elena^*

来源：Systems & Control Letters, 2014, 64: 12-19.

DOI：10.1016/j.sysconle.2013.10.008

• Positive switched systems
• Asymptotic stability
• Stabilizability
• Metzler Hurwitz matrices

Given a single-input continuous-time positive system, described by a pair (A, b), with A a diagonal matrix, we investigate under what conditions there exists a state-feedback law u(t) = c(inverted perpendicular)x(t) that makes the resulting controlled system positive and asymptotically stable, by this meaning that A + bc(inverted perpendicular) is Metzler and Hurwitz. In the second part of this note we assume that the state-space model switches among different state-feedback laws (c(i)(inverted perpendicular), i = 1, 2,..., p) each of them ensuring the positivity, and show that the asymptotic stability of this type of switched system is equivalent to the asymptotic stability of all its subsystems, while its stabilizability is equivalent to the existence of an asymptotically stable subsystem.

• 出版日期2014-2