Absolute stability of Lurie direct control systems with time-varying coefficients and multiple nonlinearities

Absolute stability of Lurie direct control systems with time-varying coefficients and multiple nonlinearities is studied in this paper. Depending on the related methods, relative magnitude of the norm-unbounded coefficients was estimated. By knowledge of nonsingular M-matrix, the Lyapunov function was constructed, and some absolute stability criteria of this kind of systems were obtained. In addition, some simple and practical corollaries were derived from the theorem of Taussky. The main contribution of this paper is that the criteria which we introduced allow for the situation that the norms of coefficient matrices are unbounded. At last, the example shows the availability of the criteria.