Stability analysis of hybrid time-delay systems using homogeneity property

A novel stability criterion and precise control for linear time delay systems based on regional configuration of the poles

This paper presents the concept of region stability and provides criteria for region stability of linear time delay systems, which can reveal the dynamic and steady-state performance of the systems more precisely. Corresponding design schemes for stabilization and tracking control that can accurately control various performance of time delay systems have also been explored. First, in the light of the connection between the poles and the dynamic properties of the system, the concept of region stability is given to describe the finer dynamic behavior of time delay systems. The criteria for the region stability are also presented. Second, the region stabilization methods are investigated, which can ensure that the system satisfies a certain dynamic performance by setting the eigenvalues in a certain convex region. Third, a precise tracking control of the linear time delay systems is addressed as an application of region stabilization. It can control the steady state performance and transient response of the tracking signal more precisely. Finally, three instances are provided to display the superiority of the new method for the performance indexes of the linear time delay systems.

Novel negative-definiteness conditions on the quadratic polynomial function with application to stability analysis of continuous time-varying delay systems

When analyzing the stability of time-varying delay systems in view of the Lyapunov-Krasovskii functional, a quadratic polynomial function with regard to time-varying delay is always generated. And it is particularly crucial to determine the negativeness of the matrix of such a quadratic form function for obtaining an analysis result expressed in linear matrix inequalities. This paper proposes a method of tangent intersection in the delay interval segmentation, producing the generalized quadratic convex conditions by further utilizing the cross point between every two tangent lines. It reduces the conservatism of the existing conditions remarkably without requiring unexplainable adjustable parameters and additional decision variables. Benefiting from the newly proposed quadratic convex conditions, the novel stability conditions are derived, the superiority of which is demonstrated through several widely used numerical instances and single area power system PI control example.