  We consider the stability and the input-output analysis problems of a class
of large-scale hybrid systems composed of continuous dynamics coupled with
discrete dynamics defined over finite alphabets, e.g., deterministic finite
state machines (DFSMs). This class of hybrid systems can be used to model
physical systems controlled by software. For such classes of systems, we use a
method based on dissipativity theory for compositional analysis that allows us
to study stability, passivity and input-output norms. We show that the
certificates of the method based on dissipativity theory can be computed by
solving a set of semi-definite programs. Nonetheless, the formulation based on
semi-definite programs become computationally intractable for relatively large
number of discrete and continuous states. We demonstrate that, for systems with
large number of states consisting of an interconnection of smaller hybrid
systems, accelerated alternating method of multipliers can be used to carry out
the computations in a scalable and distributed manner. The proposed methodology
is illustrated by an example of a system with 60 continuous states and 18
discrete states.
