Deadbeat control of linear multivariable generalized state-space systems

The classic idea of deadbeat control is extended to linear multivariable discrete-time generalized state-space systems by means of algebraic methods. The asymptotic properties of the linear quadratic regulator theory are used to obtain the classes of deadbeat controllers that utilize stabilizing full semistate feedback. The solution is constructed from a `cheap control´ problem. Both semistate and output deadbeat control laws are considered. The main design criteria are that the semistate and/or outputs of the system be driven to zero in minimum time and that the closed-loop system be internally stable. Unique properties of these types of control laws are discussed. For semistate deadbeat control, all the (dynamic) poles, including those at infinity, are moved to the origin, whereas for output deadbeat, some of the finite transmission zeros are cancelled. Numerically reliable algorithms are developed to solve both problems