Stability Margins for Multilinear Interval Systems via Phase Conditions: A Unified Approach

This paper gives a simple way of checking the stability with respect to an arbitrary stability region of a family of polynomials containing a vector of parameters varying within prescribed intervals. It is assumed that the parameters appear affine multilinearly in the characteristic polynomial coefficients. The condition proposed here is simply to check the phase difference of the vertex polynomial. This test based on the mapping theorem significantly reduces computational complexity. We omit mathematical proofs in this version. The results can be used to determine various stability margins of control systems containing interconnected interval subsystems. These include the gain, phase, time-delay, H^∞ and nonlinear sector bounded stability margins of multilinear interval systems.