Asymptotically tracking for a class of second-order descriptor dynamical systems

Model-following control problem of linear time-invariable second-order descriptor systems is considered in the paper. Sufficient and necessary conditions are presented for the existence of solutions to the problem; the condition, that is, the two combined generalized second-order Sylvester matrix equations are converted into a normal second-order Sylvester matrix equation; the controller gains are completely parameterized. The parametrical expression contains a group of parameter vectors which can be properly chosen to produce a closed-loop system with some desired system specifications. Simulation is given to show the effectiveness of this method.