Solving the Problem of an Interval System Placing Poles in Real Segments

We consider a non-stationary control system with an interval characteristic polynomial; the coefficients are specified by their intervals. For such a system, the problem of a linear robust controller modal synthesis is solved, ensuring the localization of all the system poles in segments on the real axis. This arrangement of the poles makes it possible to obtain and store monotonic transient processes in the system for any values of the polynomial coefficients from their intervals. In this case, the maximum time of the transition process is determined by the right boundary of the segment closest to the imaginary axis. To solve the problem, rules for determining the inverse images of the real pole segment boundaries are obtained for the polygon's vertices formed by the characteristic polynomial's interval coefficients. Based on the knowledge of such essential vertices, a technique has been developed for the parametric synthesis of a full order in an output modal robust controller, ensuring the segment's right boundaries and desired location of the system's real poles. A numerical example is given.