Publications Lists     [ all BibTeX ]  

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 two-dimensional (2D) discrete behaviors, dened on the grid Z+ 
Z and having the time as (rst) independent variable, are investigated. For these behaviors, by
emphasizing the causality notion that is naturally associated with the time variable, we introduce
two new concepts of controllability. Algebraic characterizations of time-controllability and of zero-
time-controllability are provided, and it is shown that behaviors endowed with these properties admit
special decompositions. Next, the dead-beat control (DBC) problem and the concept of admissible
DBC are introduced and related to the zero-time-controllability property. Dierently from what
happens with one-dimensional behaviors, zero-time-controllability does not ensure the existence of
regular DBC's, and stronger algebraic properties need to be imposed on the behavior. Finally,
necessary and sucient conditions for the existence of a DBC that makes the resulting behavior
both strongly autonomous and nilpotent are provided.

In this paper exponential stabilizability
of continuous-time positive switched systems is in-
vestigated. For two-dimensional systems, exponential
stabilizability by means of a switching control law can
be achieved if and only if there exists a Hurwitz convex
combination of the (Metzler) system matrices. In the
higher dimensional case, it is shown by means of an
example that the existence of a Hurwitz convex combi-
nation is only sufficient for exponential stabilizability,
and that such a combination can be found if and only
if there exists a smooth, positively homogeneous and
co-positive control Lyapunov function for the system.
In the general case, exponential stabilizability ensures
the existence of a concave, positively homogeneous and
co-positive control Lyapunov function, but this is not
always smooth. The results obtained in the first part
of the paper are exploited to characterize exponential
stabilizability of positive switched systems with delays,
and to provide a description of all the “switched equi-
librium points” of an affine positive switched system.

Abstract—In this paper the concepts of controllability and
zero-controllability of a variable w, appearing either in a
standard or in a latent variable description (as manifest variable),
are introduced and characterized. By assuming this perspective,
the dead-beat control (DBC) problem is posed as the problem of
designing a controller, involving both w and the latent variable
c, such that, for the resulting controlled behavior, the variable w
goes to zero in a finite number of steps in every trajectory. Zerocontrollability
of w turns out to be a necessary and sufficient
condition for the existence of “admissible” DBC’s as well as for
the existence of regular DBC’s. The class of minimal DBC’s,
namely DBC’s with the least possible number of rows, is singledout
and a parametrization of such controllers is provided. Finally,
a necessary and sufficient condition for the existence of DBC’s
that can be implemented via a feedback law, for which w is
the input and the latent variable c the corresponding output, is
provided.

In this paper we consider a supervisory control scheme for non-homogenous multi-agent systems. Each
agent is modeled through an independent strictly proper SISO state space model, and the supervisory
controller, representing the information exchange among the agents, is implemented in turn via a linear
state-space model. Controllability and observability of the overall system are characterized, and some
preliminary results about stability and stabilizability are provided. The paper extends to non-homogenous
multi-agent systems some of the results obtained in Hara et al. (2007, 2009) [4,5,7] for the homogenous
case.

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.