Preservation of stabilizability of a continuous time-invariant linear system after discretization

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Abstract
On assuming that a continuous-time time-invariant linear system (CFLS) is reachable or stabilizable, a necessary and sufficient condition is presented that the discrete-time time-invariant linear system resulting from the hold equivalence approximation to the CILS is also reachable or stabilizable. The studies are based on the eigenvalues and eigenspaces of the adjoint A∗ of the system matrix A and the kernel of the adjoint B∗ of the input matrix B appearing in the CILS. A necessary and sufficient condition for the observability or detectability of a CILS to be preserved after discretization is also sought.

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