Abstract of the talk:

Dynamics Of Switching Positive Linear Systems - Analysis Based On Row And Column Representatives

Octavian Pastravanu*, Mihaela-Hanako Matcovschi

”Gheorghe Asachi” Technical University of Iasi,

Faculty of Automatic Control and Computer Engineering

* E-mail: opastrav@ac.tuiasi.ro

Abstract: For arbitrarily switching positive linear systems (with continuous- or discrete-time dynamics), three diagonal types of copositive Lyapunov function (CLF) candidates are considered, namely: (i) linear, (ii) max-type (polyhedral), and (iii) quadratic. The existence of CLFs of form (i) - (iii) is algebraically characterized by the solvability of some matrix inequalities (associated with the switching system modes). The concrete construction of CLFs can be addressed in terms of Perron-Frobenius eigenstructure theory applied to (i) column-representatives, (ii) row-representatives, (iii) both column- and row-representatives of the constituent matrices. Given a switching system, CLFs of forms (i) and (ii) play complementary roles (in the sense that their existence is characterized independently one from the other). Forms (i) and (ii) play dual roles for the comparative analysis of primal vs. dual system dynamics. The use of representatives can be extended to the design of time-dependent CLFs – switched CLFs (in the case of discrete-time dynamics). Comparison theory also allows the exploitation of the above results for switching systems with arbitrary constituent matrices (i.e. not necessarily positive). Conditions of form (i) and (ii) applied to the comparison systems are necessary and sufficient for the invariance of rhombic and rectangular sets, respectively.

Keywords: positive systems, switching systems, stability analysis, Lyapunov functions.