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Alternative criteria for admissibility and stabilization of singular fractional order systems
Eigenstructure assignment for polynomial matrix systems ensuring normalization and impulse elimination
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Abstract
In this paper, eigenstructure assignment problems for polynomial matrix systems ensuring normalization and impulse elimination are considered. By using linearization method, a polynomial matrix system is transformed into a descriptor linear system without changing the eigenstructure of original system. By analyzing the characteristic polynomial of the desired system, the normalizable condition under feedback is given, and moreover, the parametric expressions of controller gains for eigenstructure ensuring normalization are derived by singular value decomposition. Impulse elimination in polynomial matrix systems is investigated when the normalizable condition is not satisfied. The parametric expressions of controller gains for impulse elimination ensuring finite eigenstructure assignment are formulated. The solving algorithms of corresponding controller gains for eigenstructure assignment ensuring normalization and impulse elimination are also presented. Numerical examples show the effectiveness of proposed method.
Mathematics Subject Classification: Primary: 15A18, 93B18; Secondary: 93C05.Citation: 
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Figure 1. The responses of
$ x $ and$ \dot{x} $ for normalization
Figure 2. The responses of
$ x $ and$ \dot{x} $ for impulse elimination
Figure 3. The responses of
$ {x} $ and$ \dot{x} $ for impulse elimination
Figure 4. The responses of
$ \ddot{x} $ and$ x^{(3)} $ for impulse elimination -
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Figure 1. The responses of
$ x $ and$ \dot{x} $ for normalization -
Figure 2. The responses of
$ x $ and$ \dot{x} $ for impulse elimination -
Figure 3. The responses of
$ {x} $ and$ \dot{x} $ for impulse elimination -
Figure 4. The responses of
$ \ddot{x} $ and$ x^{(3)} $ for impulse elimination