An Algorithm for Computing the Degree of Controllability of a Discrete Time, Bounded Input, Regulator Problem

This paper presents an algorithm for measuring the Degree of Controllability (DOC) for the bounded input, regulator problem of a linear, discrete, time-invariant system. The computed DOC measures the size of the discrete time Recovery Region, R(N), which contains the set of inital states that can be returned to a zero state with an admissible control within a specified time period. Specifically the algorithm computes the volume of the largest approximating hyperellipsoid, E(N), which is contined in R(N). In additon, the algorithm gives an approximate characterization of R(N), since it finds in addition to the radius of E(N), the positive definite matrix which defines the largest E(N) contained in R(N). An example is given to illustrate the improvement in the characterization of the R(N) region over the previously defined DOC´s which only defined an approximating hypersphere to R(N).