A new arithmetic of lower conservatism degree of robust stability for linear interval systems

A novel arithmetic is proposed for calculating the lower conservatism degree of robust stability for the linear uncertain systems with system matrix being interval matrix based on the theory of Gerschgorin separating the eigenvalues of matrix. And the new method transformed the arithmetic about the lower conservatism degree of robust stability for linear uncertain systems into the feasibility of the roots of constrained quadratic equations containing one unknown. The novel algorithm was attested by a second-order system and extended to the multi-order system. Then an example was analyzed, and the result shows that the new algorithm is proved to be lower conservatism, which can improve the analysis of system performance for linear uncertain systems.