A geometric framework for constraints and data: from linear systems to convex processes

In part one of this thesis we develop the theory of analyis of convex processes. The results of this development can be directly applied to the analysis of discrete time, linear, time-invariant mathematical systems with conic constraints. Such constraints arise from physical properties of natural phenomena, and hence it is important that these are considered in the mathematical models thereof. In part two we focus determining whether a system has a given system theoretic property on the basis of measured data. For this, we develop the informativity framework, which allows us to consider and resolve a large number of such problems.