Two-DOF Lifted LMI Conditions for Robust D -Stability of Polynomial Matrix Polytopes

摘要

This technical note investigates the problem of checking robust D -stability of polytopes of polynomial matrices. Lifted linear matrix inequality (LMI) conditions with two-DOF (two degree of freedom) positive integers (τ, κ) are derived to possess more flexible tradeoff between the conservatism and computational complexity. In the process of formulating the LMIs, the relevant region D is represented by a quadratic constraint in the complex plane. The matrix, composing the quadratic form with the vector of a variable, is called the region matrix. Then a variable substitution approach is put forward for the lifted LMI version by extending the dimensions of the region matrix and the Lyapunov matrix. The effectiveness and advantages of the proposed method have been illustrated by numerical examples.