Disturbance Decoupling for Singular Systems by State and Derivative Feedback and State and Derivative Output Injection

摘要

Disturbance decoupling problem for linear time invariant singular systems is analyzed. A disturbance may represent modeling or measuring errors, noise, or higher order terms in linearization. We give necessary and sufficient conditions for the existence of a solution to the disturbance decoupling problem with or without stability via a proportional and derivative feedback and proportional and derivative output injection that also makes the resulting closed-loop system regular and of index at most one. All results are based on canonical reduced forms that can be computed using a complete system of invariants that can be implemented in a numerically stable way.