Optimal symmetric ℋ2 controllers for systems with collocated sensors and actuators

This paper addresses the problem of designing the optimal symmetric ℋ₂ controller for a plant with collocated sensors and actuators but with possibly asymmetric disturbance injection and performance specification. For such a control problem, the generalized plant has a symmetric block representing the transfer matrix from the control input to the measured output. A complete solution to the optimal ℋ₂ control problem with the symmetric structural constraint is given in terms of the optimal solution to a standard ℋ₂ model matching problem without the constraint