This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a (fictitious) constraint logic programming language with explicit quantifier notation. This allows us to clarify the special structure of the problem, and to extend an algorithm for computing approximate solution sets of first-order constraints over the reals to exploit this structure. As a result we can deal with inputs that are clearly out of reach for current symbolic solvers.
A new method is presented for characterizing the set of all values of the parameters of a linear time-invariant model that are associated with a stable behavior. A formal Routh table is used to formulate the problem as one of set inversion, which is solved approximately but globally with tools borrowed from interval analysis. The method readily extends to the design of controllers stabilizing all models in a given class. > Preface Symbol index 1. Basic properties of interval arithmetic 2. Enclosures for the range of a function 3. Matrices and sublinear mappings 4. The solution of square linear systems of equations 5. Nonlinear systems of equations 6. Hull computation References Author index Subject index. 