Traditionally, Event-Triggered Control (ETC) methods are sample-and-hold control schemes that implement a triggering condition in order to reduce the number of control updates. Given a decay rate of the Lyapunov function, they focus on minimizing the (average) Inter-Sample Time (IST). In this thesis, we focused on the scheduling of Periodic Event-Triggered Control (PETC) controllers. By dynamically switching between triggering conditions, we
are maximizing the average rate of decay of the Common Lyapunov Function (CLF) given a minimum Average Inter Sample Time (AIST) or burst condition.

Given the physical system, we construct a switched system which captures all possible
scheduling behaviors. The l-complete abstraction of the switched system is constructed by solving a conjunction of quadratic equations. By setting a minimum AIST or burst condition, a set of states in the abstraction is marked and a safety game is played to construct the Maximal Permissive Controller (MPC).

On the safe behaviors inside the MPC, the guaranteed minimum control performance is maximized for the infinite horizon problem, i.e. by maximizing the minimum weighted time average of the primitive cycles in the MPC. First, several energy games are played to estimate
the maximum control performance. Thereafter, a mean-payoff game is played to generate the strategy securing this maximum control performance, which is used to construct the infinite horizon controller.

In this project, an positive integer addition algorithm for quantum computing is analyzed which does not makes use of carry bits. The paper shows a general parallelization method. Using this method, the circuit runs in O(n) time instead of O(n^2). The algorithm is executed with different input sizes and error rates such that usable values are found.