On the sylvester-type matrix difference systems and the controllability and observability of the time-invariant systems

The theory of difference equations is much wealthier than its counterpart in differential equations. With the emergence of digital signal processing technology, the theory of difference equations assumes great importance in areas such as digital control, image processing, and digital filter design. In this talk, a first-order matrix Sylvester difference system with a control structure is discussed in view of the existence and uniqueness of its general solution. Results are used in the study of controllability and observability of the matrix difference system coupled with an output structure. More general criteria, such as the one-sided controllability matrices and the observability Gramian, are obtained for complete controllability and complete observability of time-invariant systems.