Research Projects

This research project deals with investigating the necessary and sufficient conditions for the existence of a Luenberger observer for rectangular singular control systems with unknown inputs. Singular control systems are also known as descriptor systems and differential algebraic equations (DAEs). The project starts with analyzing the properties of singular control systems in rectangular form and their appearance in physical processes. Presence of unknown inputs in the system will play a crucial role throughout the project duration. Matrix theory approach and purely linear algebraic approaches (in the form of spaces and subspaces) will be applied to develop results. Internal structure of singular systems will be studied by applying various orthogonal decompositions of system matrices. In some recent works, use of Wong sequences is increased to understand the linear singular systems. Wong sequences will further be applied to singular control systems with unknown inputs. This will show the effects of unknown inputs or disturbances on the system clearly. In the second phase of the project, different types of observer design techniques will be studied. Simulation results will be compared through high performance computing. Necessary and sufficient condition for the existence of observers for rectangular singular control systems with unknown inputs will be derived. The third phase of the project starts with designing of minimal ordered observers for the underlying systems. Singular value decomposition (SVD) will be used to minimize the order of the observer. Necessary and sufficient conditions for the existence of the observer will be developed in terms of Wong sequences. At the end, some real-life applications will be investigated and theory will be applied to physical processes, especially to electrical and chemical systems.