Eigenvalue assignment using matrix sign functions

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1975

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Abstract

The powerful method for the solution of the algebraic Riccati equation developed by Denman and Beavers, [Math. Biosci., Vol 20], proved to be a very efficient tool in the solution of many problems of filtering and control. One of the problems that can be solved by this method is the assignment of the closed loop eigenvalues in the linear multivariable systems by state feedback. This thesis is in general concerned with the problem of pole assignment via linear state variable feedback and in particular with the inverse problem of optimal control. An algebraic Riccati equation which the weightings matrix for the states has to satisfy is derived. New method of assignment of the closed loop poles is presented and examples are given. It was shown that this design is suboptimal. The matrix P that is used to form the linear state variable feedback is obtained as a solution to an algebraic Riccati equation.

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