This paper is devoted to the study of the problem of stabilization by proportional-plus-derivative state feedback for multivariable linear time-invariant systems. In particular, explicit necessary and sufficient conditions are established for the stability of a closed-loop system obtained by proportional-plus-derivative state feedback from the given multivariable linear time-invariant system. A procedure is given for the computation of stabilizing proportional- plus-derivative state feedback. Our approach is based on properties of real and polynomial matrices.
In this paper the explicit necessary and sufficient conditions for the existence of Luenberger reduced order observer are established. In particular, it is proven that for the given linear time-invariant system of order n, having p linearly independent out- puts and m inputs, a Luenberger observer of order (n − p) can be constructed if and only if the given system is detectable. Further- more, a procedure is given for the construction of the observer. Our approach is based on the properties of real and polynomial matrices.
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