Abstract
Methods which calculate state feedback matrices explicitly for uncontrollable systems are considered in this paper. They are based on the well-known method of the entire eigenstructure assignment. The use of a particular similarity transformation exposes certain intrinsic properties of the closed loop w-eigenvectors together with their companion z-vectors. The methods are extended further to deal with multi-input control systems. Existence of eigenvectors solution is established. A differentiation property of the z-vectors is proved for the repeated eigenvalues assignment case. Two examples are worked out in detail.
Highlights
A study by [1] on eigenvalue assignment for single-input linear systems is followed in this paper
It is based on the well-known entire eigenstructure assignment method [2]-[4]
N.B.; The state feedback matrix above assigns the four eigenvalues required according to the entire eigenstructure method
Summary
A study by [1] on eigenvalue assignment for single-input linear systems is followed in this paper. Studies regarding existence, uniqueness, and numerical solution have been conducted by [9] As required by this method, the w-eigenvectors and companion z-vectors are extracted out of the null space of an augmented n× n + m matrix. For the single-input and multi-input cases, the study shows that calculations of the needed w-eigenvectors and the z-vectors are based on lower order matrices specifying the controllable part and the uncontrollable part of the system. Such approach simplifies the design process, and provides numerical advantages.
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