Relational Systems

This chapter is concerned with analysis and decision making problems for a static input—output plant described by a relation which is not reduced to the function 0 considered in Sect. 1.3. Consequently, for the given relation, the output is not determined by the input. The analysis problem consists in finding the output property (or the set of possible outputs) for the given input property (or the given set of inputs), and the decision problem consists in finding the input property (or the set of possible inputs) for the given output property (or the set of acceptable outputs, required by a user). For the functional plant presented in Sect. 1.3, the input and output properties have the form “ u = u* ” and “ y = y* ”, respectively. For the relational plant the respective properties have the form “ u ∈ D _u ” and “ y ∈ D _y ” where D _u and D _y are subsets of U and Y, respectively.