Upper bounds of the deviations in linear dynamical system with bounded disturbances

A practically significant effect of a surge occurrences in linear dynamical systems under nonzero initial conditions is explored. The linear dynamical system subjected to unknown-but-bounded exogenous disturbances is considered. Using the apparatus of linear matrix inequalities and the invariant ellipsoids concept, the estimations of the upper bounds of the trajectories deviations are obtained, and an approach is suggested to the feedback design that minimizes the deviations. The efficacy of the approach proposed is illustrated on numerical examples.