The stability analysis and simulation of linear systems via LMI

By inequality analysis, this paper deals with the stability of linear system. First of all, by constructing suitable Lyapunov functionals, a new simple sufficient condition is presented for the linear system based on LMI. Next, the sufficient condition of the state feedback system will be given, and the problem of determining the maximum time-delay under which the system will remain stable is cast into a generalized eigenvalue problem solved by LMI toolbox in MATLAB. Finally, two illustrative examples are given to demonstrate the effectiveness and convenience of the proposed method.