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In the paper output feedback control of Boolean control networks (BCNs) is investigated. First, necessary and sufficient
conditions for the existence of a time-invariant output feedback (TIOF) law, stabilizing the BCN to some equilibrium point,
are given, and constructive algorithms to test the existence of such a feedback law are proposed. Two sufficient conditions for
the existence of a stabilizing time-varying output feedback (TVOF) are then given. Finally, an example concerning the lac
Operon in the bacterium Escherichia Coli is presented, to illustrate the effectiveness of the proposed techniques.

In this paper we consider discrete-time positive switched systems, switching among autonomous
subsystems, characterized either by monomial matrices or by circulant matrices. For these two classes of
systems, some interesting necessary and sufficient conditions for (global uniform) asymptotic stability
and stabilizability are provided. Such conditions lead to simple algorithms that allow to easily detect,
under suitable conditions, whether a given positive switched system is not stabilizable.

Abstract—The aim of this paper is to introduce and characterize
observability and reconstructibility properties for Boolean
networks and Boolean control networks, described according to
the algebraic approach proposed by D. Cheng and co-authors in
the series of papers [3], [6], [7] and in the recent monography
[8]. A complete characterization of these properties, based both
on the Boolean matrices involved in the network description and
on the corresponding digraphs, is provided. Finally, the problem
of state observer design for reconstructible BNs and BCNs is
addressed, and two different solutions are proposed.

In this note we rst characterize the periodic trajectories (or, equivalently, the limit cycles) of a Boolean network, and their global attractiveness. We then investigate under which conditions all the trajectories of a Boolean control network may be forced to converge to the same periodic trajectory. If every trajectory can be driven to such a periodic trajectory, this is possible by means of a feedback control law.

In this paper we consider the class of discretetime
switched systems switching between p autonomous positive
subsystems. First, sufficient conditions for testing stability, based
on the existence of special classes of common Lyapunov functions,
are investigated, and these conditions are mutually related, thus
proving that if a linear copositive common Lyapunov function can
be found, then a quadratic positive definite common function can
be found, too, and this latter, in turn, ensures the existence of a
quadratic copositive common function. Secondly, stabilizability
is introduced and characterized. It is shown that if these
systems are stabilizable, they can be stabilized by means of a
periodic switching sequence, which asymptotically drives to zero
every positive initial state. Conditions for the existence of statedependent
stabilizing switching laws, based on the values of a
copositive (linear/quadratic) Lyapunov function, are investigated
and mutually related, too.
Finally, some properties of the patterns of the stabilizing
switching sequences are investigated, and the relationship between
a sufficient condition for stabilizability (the existence of
a Schur convex combination of the subsystem matrices) and an
equivalent condition for stabilizability (the existence of a Schur
matrix product of the subsystem matrices) is explored.