Stability analysis for interconnected systems with “mixed” negative-imaginary and passivity

This paper presents an analytical framework to examine the unconditional stability of two stable, linear timeinvariant systems in a positive feedback interconnection where one system has “mixed” negative-imaginary and passivity properties and other system has “mixed” negative-imaginary and negative-passivity properties. The examination of the stability of above mentioned interconnection is done by using a Nyquist criteria, and it is shown that the positive feedback interconnection between such two systems is guaranteed to be finite-gain stable. A numerical example is presented in the paper to demonstrate the usefulness of the proposed analytical framework.