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**Additional resources for Applications of integer quadratic programming in control and communication**

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In [58, 59], the equivalence between the following five classes of hybrid systems is, under certain conditions, established: MLD systems, Linear Complementarity (LC) systems, Extended Linear Complementarity (ELC) systems, PWA systems and Max-Min-PlusScaling (MMPS) systems. The equivalence result between MMPS systems and PWA systems is refined in [36]. The important result of these equivalences is that derived theoretical properties and tools can easily be transferred from one class to another, [24].

A commonly used commercial software is CPLEX. 2 Branch and Bound If computational burden is not considered, the most straightforward approach to compute the optimal solution to an optimization problem involving binary variables is to enumerate all possible combinations of the binary variables, and for each such combination, compute the optimal solution of any real variables also included in the problem. Thereafter, the objective function values are compared and the solution, or solutions, generating the best objective function value is taken as the optimal solution.

1) is used to calculate how the system will react to control inputs and thereby what will happen in the future if a certain control input is applied to the system. Not surprisingly, N is called the prediction horizon, which in practice is chosen long enough to cover a normal transient of the controlled system. 3) on the form of a formal optimization problem. The most common variants are presented and evaluated in [67]. 4), for which there exist well developed optimization routines. Hence, for linear MPC the optimization problem is considered easy to solve.