## Section: New Results

### Stability and control design of asynchronous interconnected systems

#### Passivity design for asynchronous feedback-interconnected systems

Participants : C. Canudas de Wit [ Contact person ] , F. Rubio, M. Lopez-Matinez [ University of Sevilla ] .

In this topic we have studied the passivity properties of asynchronously non-uniformly sampled systems. The idea of studying these systems comes from the necessity of developing theoretical tools for the analysis of systems that are asynchronously interconnected. Imposing certain passivity properties to each sub-system it is possible to design a local controller for each sub-system disregarding the particular characteristic of the other system (modular design).

Further studies consider systems that are either Input/Output
Strictly passive (IOSP), or systems which have bounded L_{2} -gains
less than one. The analysis is performed by using the concept of
MAximum Sampling time preserving Dissipation (MASD), for each
interconnected system. We investigate the impact of using the
scattering transformation in the computation of the MASD, and we
provide a numerical algorithm (based on a set of LMI's) that allows
to choose the most suitable configuration for the interconnection
(see [32] )

#### Stability of sampled-data systems: an input delay approach

Participant : A. Seuret.

NCS are controlled systems containing several distributed plants which are connected through a communication network. In such applications, a heavy temporary load of computation in a processor can corrupt the sampling period of a certain controller. The variations of the sampling period will affect the stability properties. It is now reasonable to design controllers which guarantee the robustness of the solutions of the closed loop system under periodic samplings. However the case of asynchronous samplings still leads to several open problems such that the guarantee of stability whatever the sampling period lying in an interval. In [38] , we propose a novel approach to obtain sufficient asymptotic and exponential stability conditions of linear time-varying systems. Those conditions are based on the continuous-time approach, [57] , and the stability of impulsive systems [67] . The proposed theorems provide larger upper-bounds of the allowable sampling period than the existing ones (based on the continuous time approach).

#### Event-based control design

Participants : N. Marchand [ Contact person ] , S. Durand.

Asynchronicity is becoming more and more meaningful in modern
control architectures and some new control strategies are being
developed by some research teams in the world. The principle of
these control laws is to compute a new control signal only when some
event occur, where an event characterizes a change in the system and
therefore a need for a new control. These approaches are supposed to
reduce the number of times the control signal is computed and to
remove the real-time hard constraint on the computational system. In
this domain, our contribution is twice. First, based on previous
result from Nicolas Marchand [5] , we proposed a
fully asynchronous control scheme (without any time information) for
chain of integrators that insures the global stability of the system
with only measures when the states cross an *a priori*
defined level. This work was presented at the IFAC world congress in
Korea [6] . Secondly, we removed the safety
limit condition introduced by K-E. Årzén in his event-based
PID controller [51] . This safety limit was added to
prevent the system to be sampled less than what Shannon theorem
requires but we showed that the Shannon sampling condition is no
more consistent in the context of event based systems. This work led
to two papers [29] ,
[18] .