Linear systems with state and control constraints: the theory and application of maximal output admissible sets

The initial state of an unforced linear system is output admissible with respect to a constraint set Y if the resulting output function satisfies the pointwise-in-time condition y(t)∈Y, t⩾0. The set of all possible such initial conditions is the maximal output admissible set O_∞. The properties of O_∞ and its characterization are investigated. In the discrete-time case, it is generally possible to represent O_∞ or a close approximation of it, by a finite number of functional inequalities. Practical algorithms for generating the functions are described. In the continuous-time case simple representations of the maximal output admissible set are not available, however, it is shown that the discrete-time results may be used to obtain approximate representations