Input-output block decoupling of linear time-varying singular systems

The input–output block decoupling problem by state feedback is studied for linear time-varying singular systems. First, an algorithm, the regularization algorithm, is developed such that the system can be made by state feedback to have a unique impulse-free solution. Second, another algorithm, the block decoupling algorithm, is proposed, which provides sufficient conditions for the solvability of the input–output block decoupling problem. Then, a decoupling feedback law is constructed such that the corresponding closed-loop system is regular, impulse-free, and noninteractive. Finally, an example is given to illustrate the applicability of the algorithms.