LMIs in Control/pages/Generalized Lyapunov Theorem

WIP, Description in progress The theorem can be viewed as a true essential generalization of the well-known continuous- and discrete-time Lyapunov theorems. Kronecker Product The Kronecker Product of a pair of matrices and is defined as follows: . Lemma 1: Manipulation Rules of Kronecker Product Let be matrices with appropriate dimensions. Then, the Kronecker product has the following properties: ; Theorem In terms of Kronecker products, the following theorem gives the -stability condition for the general LMI region case: Let be an LMI region, whose characteristic function is Then, a matrix is $\mathbb{D}_{L,M}$-stable if and only if there exists symmetric positive definite matrix such that , where represents the Kronecker product. Lemma 2 Given two LMI regions and , a matrix is both -stable and -stable if there exists a positive definite matrix , such that and . WIP, additional references to be added External Links A list of references documenting and validating the LMI. Return to Main Page: