In this paper the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms. The technique can be used to prove the stability of switched linear systems, classes of linear time-varying systems and linear differential lnclusions. We also present preliminary results on another related problem; namely, the construction of multiple polyhedral Lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems.

Self-managing solutions have recently attracted a lot of interest from the database community. The need for self-* properties is more evident in distributed applications comprising heterogeneous and autonomous databases and functionality providers. Such resources are typically exposed as Web Services (WSs), which encapsulate remote DBMSs and functions called from within database queries. In this setting, database queries are over WSs, and the data transfer cost becomes the main bottleneck. To reduce this cost, data is shipped to and from WSs in chunks; however the optimum chunk size is volatile, depending on both the resources' runtime properties and the query. In this paper we propose a robust control theoretical solution to the problem of optimizing the data transfer in queries over WSs, by continuously tuning at runtime the block size and thus tracking the optimum point. Also, we develop online system identification mechanisms that are capable of estimating the optimum block size analytically. Both contributions are evaluated via both empirical experimentation in a real environment and simulations, and have been proved to be more effective and efficient than static solutions.