Spreadability and vulnerability of distributed parameter systems

Regional Stability and Stability Radius

“…For such a systems it would be interesting to develop all the other problems of robust control through a regional aspect. For example as each zone σ ⊂ Ω has its own stability radius we can introduce the concept of vulnerability [3,5,17] to stability (A given zone σ 1 will be "more vulnerable to stability" than σ 2 if its stability radius r σ1 ≤ r σ2 ). Consequently we can consider problems of robust control (optimal) through the "more" vulnerable zone.…”

“…Also can we compare the degree of stability (of such a regions) and determine which region is the most vulnerable to instability ? [3,5] (3) For two regions σ 1 and σ 2 , can the destabilization of the one of them cause the destabilization of the other? This paper is organized as follow: In the first section we recall the stability radius.…”

Spreadability, Vulnerability and Protector Control

“…In both cases it can reach σ. We have the following characterization: (F (., s, t)) adapted to the evolution of (S) and t 1 ∈ I such that: For more details about spreadability see [4,5,8,9] and vulnerability [3,6]. An application to the groundwater pollution is given in [2].…”

“…The concept of spreadability was introduced by A. El Jai and K. Kassara [7] and developed by A. Bernoussi and A. El Jai [4,5]. Later the concept of vulnerability was introduced by A. Bernoussi and M. Amharref [6], [3] in order to characterize the zones which can be reached by a given property P (pollution for example). In addition, L Afifi et al introduced in [1] the remediability concept.…”

Protector control: Extension to a class of nonlinear distributed systems

“…Hence, this leads to the problem of the influence of this disturbance on some given areas, and also the possibility of subjecting them to controls to achieve some specified objectives. Indeed, given a fixed zone in the global domain on which the system evolves, this zone is called vulnerable if it is likely to be reached (infected) by a given property (Bernoussi and Amharref, 2003;Bernoussi, 2007). Moreover, if this zone is reached, then the problem of determining a control which makes it possible to compensate the disturbance effects on such a zone at a certain time is regional remediability.…”