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Relationship between the controllability grammian and closed-loop eigenvalues: the single input case

Pradhan, S and Modi, VJ and Bhat, MS (1993) Relationship between the controllability grammian and closed-loop eigenvalues: the single input case. In: International Journal of Systems Science, 24 (6). pp. 1133-1144.

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The controllability grammian is important in many control applications. Given a set of closed-loop eigenvalues the corresponding controllability grammian can be obtained by computing the controller which assigns the eigenvalues and then by solving the Lyapunov equation that defines the grammian. The relationship between the controllability grammian, resulting from state feedback, and the closed-loop eigenvalues of a single input linear time invariant (LTI) system is obtained. The proposed methodology does not require the computation of the controller that assigns the specified eigenvalues. The closed-loop system matrix is obtained from the knowledge of the open-loop system matrix, control influence matrix and the specified closed-loop eigenvalues. Knowing the closed-loop system matrix, the grammian is then obtained from the solution of the Lyapunov equation that defines it. Finally the proposed idea is extended to find the state covariance matrix for a specified set of closed-loop eigenvalues (without computing the controller), due to impulsive input in the disturbance channel and to solve the eigenvalue assignment problem for the single input case.

Item Type: Journal Article
Publication: International Journal of Systems Science
Publisher: Taylor and Francis Group
Additional Information: Copyright of this article belongs to Taylor and Francis Group.
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 14 Mar 2011 08:44
Last Modified: 14 Mar 2011 08:44
URI: http://eprints.iisc.ac.in/id/eprint/35730

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