The research entitled “Analysis and Design of Input-Output Group Decoupling Problems for Regular Linear Descriptor System with Index One” was conducted by **Arman** under the guidance of Dr.rer.nat. Ari Suparwanto, M.Si. and Prof. Salmah, M.Si. in 2018.

The following is the abstract of this research.

**ABSTRACT**

In the control systems, every input is generally controls more than one output and every output can be controlled by more than one input. Such a system is called coupled system. In general, the coupling system is very difficult to control. It is also known that not all coupling systems can be converted into a decoupling system. Therefore it is necessary to design some compensator such that the coupling system can be converted into a decoupling system in the sense that every input controls only one output and every output is controlled by only one input. This problem is called the input-output decoupling problem.

In this research, the input-output decoupling problem for linear descriptor system was studied using geometric approach through controllability subspace. First, the necessary and sufficient condition for the input-output group decoupling of regular linear descriptor systems of index one is established. Furthermore, the characterization of the input-output group decoupling yields an equivalent forms for the input-output group decoupling of linear descriptor system with index one.

Then, based on the standard decomposition form, we discussed the problem of group decoupled structure for slow and fast subsystems using the controllability subspace. This construction presented some results that yield a matrix structure of group decoupled system for regular linear descriptor systems of index one. System with such structure is called the normal form for input-output group decoupling. The normal form of input-output group decoupling can be considered as an input-output decoupling system which is controllable consists of independently controllable subsystems.

**Key words:** linear descriptor systems, group decoupling, controllable subspaces