Stability and stabilizability of linear time-invariant interval systems.

In this paper, some new approaches for stability and stabilizability determination as well as state feedback stabilization controllers of linear time-invariant (LTI) interval systems are proposed. The presented stability conditions are less conservative than those of Kharitonov's theorem, and Gerschgorin's disc theorem methods. Moreover, some of the proposed stability, stabilizability, and feedback stabilization control methods for LTI interval systems are proved to be sufficient and necessary conditions. Compared with some traditional stability analysis and feedback stabilization design methods for LTI interval systems, these new approaches have lower computational complexity because of a special form of parameter vertex matrices developed in this work. Some numerical and practical examples are given to demonstrate the effectiveness and advantages of the proposed methods.