This paper discusses the stability problem of linear continuous-time distributed systems. When dealing with large-scale systems, usually there is not thorough knowledge of the interconnection models between different parts of the entire system. In this case, a useful stability analysis method should be able to deal with high dimensional systems accompanied with bounded uncertainties for its interconnections. In this paper, in order to formulate the stability criterion for large-scale systems, stability analysis of LTI systems is first considered. Based on the existing methods for estimating the spectra of square matrices, sufficient criteria are proposed to guarantee the asymptotic stability of such systems. One of the advantages of these stability conditions is in analyzing linear systems having uncertainties. In this case, a new sufficient criterion is introduced. Back to the main purpose of the paper, it will be proved that the method can also be used for the stability investigation of large-scale systems accompanied with bounded time-variant uncertainties. Then the maximum permissible bounds for the interconnections while holding the stability will be obtained. Since in analyzing large-scale systems there is hardly thorough knowledge about the interactions between sub- systems, finding such bounds is of great importance. Unlike most of the previous work, this method is not restricted to structured uncertainties belonging to convex sets. The merit of the suggested stability analysis is illustrated via several examples.
Shekaramiz, Mohammad, "On the Stability Analysis of Linear Continuous-Time Distributed Systems" (2018). Electrical and Computer Engineering Faculty Publications. Paper 213.