An approach for computing the exact stability domain for a class of LTI parameter dependent systems

In this paper, the complete stability domain for both single- and multi-parameter dependent LTI systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The single parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity of the results presented in this paper.