The theorems associated with the observability matrices and gramians play a crucial role in both analysis and design of control systems. This paper presents the development of these theorems and their proofs in the context of a computationally attractive system model. This is accomplished by incorpo rating the structural properties of the model into the theorems that are found in the literature. The developed theorems lead to a generalized form of the Liapunov equation. An analytical solution for this equation is also presented. Finally, an example is given to illustrate the application of the proposed theorems.
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