The problem of tracking for second-order dynamical systems subject to disturbance input is considered by using a complete parametric design approach. The goal of this problem is to design a controller such that the output of the controlled system robustly asymptotically tracks the output of the reference model, and the transfer function from the exogenous disturbance to the tracking error meets a prescribed norm upper bound constraint. Based on the complete parametric solution to a class of generalized second-order Sylvester matrix equations, complete parameterizations for all the controller gain matrices are established in terms of two set of freedom parameters. Also, based on these parametric gain matrices, the prescribed norm upper bound constraint is transformed into an equivalent constraint condition which restricts the choice of the freedom parameters. An example is utilized to show the effect of the proposed approach.
Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix
