*Article* **The Dual Characterization of Structured and Skewed Structured Singular Values**

**Mutti-Ur Rehman 1,2,†, Jehad Alzabut 3,4,†, Taqwa Ateeq 5, Jutarat Kongson 6,\* and Weerawat Sudsutad <sup>7</sup>**


**Abstract:** The structured singular values and skewed structured singular values are the well-known mathematical quantities and bridge the gap between linear algebra and system theory. It is wellknown fact that an exact computation of these quantities is NP-hard. The NP-hard nature of structured singular values and skewed structured singular values allow us to provide an estimations of lower and upper bounds which guarantee the stability and instability of feedback systems in control. In this paper, we present new results on the dual characterization of structured singular values and skewed structured singular values. The results on the estimation of upper bounds for these two quantities are also computed.

**Keywords:** eigenvalues; singular values; structured singular values; skewed structured singular values

**MSC:** 15A18; 15A03; 05B20; 15A23
