This report is the second deliverable D7.2 of Work Package WP7 of the HYBRIDGE Project. The main contributions of D7.2 is a review of the concept of observability for hybrid systems and the presentation of a new approach to observability and observer design for hybrid systems. The ...rst part of the report deals with a formal de...nition of hybrid system that is used to present in a uni...ed fr...

Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise is present in the system.

Hybrid systems are systems with interacting discrete and continuous dynamics. They are models for understanding, e.g., computer systems interfacing with the physical environment. Hybrid systems have a complete axiomatization in differential dynamic logic relative to continuous systems. They also have a complete axiomatization relative to discrete systems. Moreover, there is a constructive reduc...

The notions of finite analytic partition, dynamical consistency, and partition machine were originally developed in (Wei 1995; Caines &: Wei 1998) for dynamical systems on differentiable manifolds and in (Caines &~ Lemch 1999) for hybrid systems; in this paper they are generalized to hybrid systems with disturbances.

Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of ! limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and non-Zeno hybrid systems can be treated within the same framework. As an example, LaSalle's Invariance Principle is extended to hybrid systems. Zeno hybrid systems are dis...

Nowadays, dust phenomenon is one of the important challenges in warm and dry areas. Forecasting the phenomenon before its occurrence helps to take precautionary steps to prevent its consequences. Fuzzy expert systems capabilities have been taken into account to assist and cope with the uncertainty associated to complex environments such as dust forecasting problem. This paper presents novel hyb...