Optimal Feedback Selection for Structurally Cyclic Systems with Dedicated Actuators and Sensors

This paper solves the sparsest feedback selection problem for linear time invariant structured systems, a long-standing open problem in structured systems. We consider structurally cyclic systems with dedicated inputs and outputs. We prove that finding a sparsest feedback selection is of linear complexity for the case of structurally cyclic systems with dedicated inputs and outputs. This problem has received attention recently but key errors in the hardness-proofs have resulted in an erroneous conclusion there. This is also elaborated in this brief paper together with a counter-example.