Stability analysis and control of linear neutral systems based on method of semi-discretization

This paper mainly considers the stability analysis and control of linear neutral systems with multiple time-delays. Using the method of semi-discretization, we can analyze the stability of linear neutral systems described by ordinary differential equations (ODEs). Method of semi-discretization provides us with an effective way to obtain an arbitrary linear neutral system's transition matrices, which can be multiplied together to get the mapping matrix. By comparing the maximum eigenvalue of the mapping matrix with 1, we can conclude whether this system is asymptotically stable. Furthermore, this method can also be used to minimize the maximum eigenvalue, and optimal control gains for linear neutral systems are obtained simultaneously. Several numerical examples are given to illustrate the effectiveness of this method.