• International Journal of Control, Automation, and Systems
• /
• v.2 no.4
• /
• pp.516-522
• /
• 2004

In this paper we investigate the properties of a generalized impulse response Gramian. The recursive relationship satisfied by the family of Gramians is established. It is shown that the generalized impulse response Gramian contains information on the characteristic polynomial of a linear time-invariant continuous system. The results are applied to model reduction problem.

• International Journal of Control, Automation, and Systems
• /
• v.2 no.3
• /
• pp.384-389
• /
• 2004

Recently a method of model reduction for discrete systems has been proposed in the literature based on a new impulse response Gramian. In this method, the system matrix$A_r$ of a reduced model is computed by approximating the reduced-order impulse response Gramian. The remaining matrices $b_r$ and $c_r$ are obtained so that various initial Markov parameters and time-moments of the original system are preserved in the reduced model. In this paper a different approach is presented based on the recursive relationship among the impulse response Gramians.