This paper mainly deals with the stability problem of continuous-time linear systems having uncertainties. Instead of using the tradition types of Lyapunov functions, this paper provides a very different method to investigate the stability of such systems. Hence, it reduces the conservativeness of having structured uncertainties belonging to convex sets. Based on a famous theorem that specifies regions containing all the eigenvalues of a complex square matrix, sufficient criteria are proposed to guarantee the asymptotic stability of linear systems. The main merit of this method is in analyzing linear systems having uncertainties. Moreover, the proposed criteria can also be used to investigate the stability of linear time-variant systems. In this case, a new stability criterion has been introduced. Finally, a rectangular region has been obtained which illustrates the region including spectra of the state matrix of any linear system even those having uncertainties. The usefulness of the suggested stability criteria and the proposed rectangular regions have been illustrated by several examples.
Shekaramiz, Mohammad, "Simple Stability Criteria for Uncertain Continuous-Time Linear Systems" (2019). Electrical and Computer Engineering Faculty Publications. Paper 214.