Markovsky, Ivan and Rao, Shodhan
Palindromic polynomials, time-reversible systems, and conserved quantities.
In, 16th Mediterranean Conference on Control and Automation, Congress Centre, Ajaccio, France,
25 - 27 Jun 2008.
The roots of palindromic and antipalindromic polynomials appear in pairs (s,1/s). A polynomial with such roots is antipalindromic if and only if in addition, it has a root at 1 of an odd multiplicity. The result has applications in system theory: 1) any kernel representation of a discrete-time, time-reversible, scalar, autonomous LTI system is either palindromic or antipalindromic. (Similar statement holds for systems with inputs.) 2) LTI systems with palindromic or antipalindromic kernel representations have nontrivial conserved quantities.
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