Robust pole assignment for interval polynomial based on positive interval Routh-table: positive property of Routh-table of binomial coefficients

Abstract

This paper elucidates a robust pole assignment (RPA) scheme for an interval polynomial based on positive interval Routh-table using a binomial coefficients feedback gain. The robust scheme transforms the problem of RPA into the problem of solving a family of stability condition polynomials that have positive function values. The condition for the existence of solution is that all entries of the Routh-table of binomial coefficients (RTBC) are positive. Importantly, this paper provides an advanced general formula for the generated entries of the RTBC, confirming that all entries of RTBC are positive. An illustrative example reveals the effectiveness of the scheme.

Keywords:

• robust pole assignment
• interval polynomial
• Routh-table of binomial coefficients
• positive interval Routh-table

Acknowledgment

I would like to thank the reviewers for their detailed suggestions for the improvement of the manuscript.