Simultaneous Stabilization for Unstable Multi-Input Multi-Output Plants

What is it about?

The solution to the simultaneous stabilization problem of a finite set of MIMO unstable plants considered in this note is based on the frequency-shaped central plant and its sufficiency condition for simultaneous stabilization. The novel method proposed in this Note to acquire the frequency-shaped central plant from a finite set of MIMO unstable plants used v-gap metric between the plants, the frequency shaping of the plants that used the pre- and post-compensators, and the robust stabilization theory. An optimization problem is formulated to obtain the pre- and post-compensators that reduce the minimum among the maximum v-gap metrics of all the frequency-shaped plants as well as induce required frequency characteristics on all the plants in the set without instigating pole-zero cancellation with any plants in the set. A novel iterative algorithm is developed to solve this optimization problem to attain the compensators. The plant with a maximum v-gap metric that is the minimum among the maximum v-gap metrics of all the frequency-shaped plants is identified as the frequency-shaped central plant. Also, the sufficiency condition of the frequency-shaped central plant is the most suitable sufficiency condition for the simultaneous stabilization. The capability of the iterative algorithm presented in this note is demonstrated by a realistic design example.

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