A new metric for measuring the distance between two linear systems

Measuring the distance between two linear time invariant systems (LTIs) and its application are investigated by a very common and useful method (v-gap metric) and in following some related problems are raised. In many times we are interested in comparing two linear systems with their different frequency ranges and it is essence to have a metric which could cover all over frequency ranges of two plants. So by keeping the same topology of v-gap metric, a new metric is defined to measure distance between two linear systems. This metric is the extension of the v-gap metric on the linear systems from H_∞ norm to H₂ norm space. It is shown that all relations and equations which are used in v-gap can be proof in new space. The new metric not only has the ability of standard v-gap metric for measuring distance but also has some advantages. In addition by some simulations these two metrics are compared.