Stability of interconnection, dissipativity and mixing

摘要

In this paper, we have characterized a set of linear controllers to guarantee a stable interconnection with a given plant. We consider the plant to be dissipative with respect to a general power supply, which satisfies a spectral factorizability condition. We show in this paper that the interconnection of the plant with a controller is guaranteed to be stable if we choose a controller that is also dissipative with respect to a new supply rate. This new supply rate is determined by the supply rate of the plant and the interconnection topology. We further show how this result can be applied to special cases of Nyquist-plot-compatible supply rates and supply rates that are obtained by mixing two different supply rates. An upshot of the material presented in this paper is that stability assurance due to passivity, small-gain, negative imaginary, and their mixtures are all special cases of stability due to dissipativity.