A new generator of causal ideal internal dynamics for a class of unstable linear differential equations

The generator design for causal ideal internal dynamics (IID), namely, solving IID, is a fundamental problem in a nonminimum-phase output tracking process. In this paper, for a class of unstable matrix differential equations, a new causal IID generator is proposed, whose parameters are partly chosen via H₂=H_∞ optimization. Compared with existing similar design schemes, it is applicable to matrix differential equations with singular system matrices. Also, it requires less computation, avoids taking higher order derivatives, and can be easily extended to treat slowly time-varying matrix differential equations without the need for extra computation.