• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.71-77
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• 1995

The control effectiveness and disturbance suppressibility are mainly governed by a left eigenstructure of a system. In this paper, a control algorithm which uses an output feedback eigenstructure assignment scheme is proposed in order that a desired closed-loop system has the specified degree of controllability and/or degree of disturbance suppressibility. To do this, a modal and a gross disturbance suppressibility measures are proposed. A modified version of Hamdan and Nayfeh's modal controllability measure is also presented. The validity and usefulness of the proposed measures and the controller design algorithm are illustrated by designing a controller for a third-order system as an example.