Approach to pole assignment by centralised and decentralised output feedback

The paper presents a method for output feedback pole assignment in both centralised and decentralised systems. For the nth-order m-input l-output system (A, B, C), the existence of a solution to the pole-assignment problem is determined by checking the rank of a certain matrix E formed from the matrices CAⁱB, i=0, 1, . . ., n-1. It is shown that when rank(E)=n, it is possible to assign min(n, ml) poles by constant output feedback. The solution to the nonlinear equations required for pole assignment is obtained by, first, converting the nonlinear equations into a set of linear equations and, then, applying an iterative numerical method. The pole assignment condition and the method of solution are extended to decentralised systems using constant or dynamic output feedback. In particular, it is shown that, when an N-station decentralised system satisfies a certain rank condition, min(n, Sigma ,_j=1^Nm_jl_j) poles can be assigned using decentralised constant output feedback, where m_j and l_j are the number of local inputs and outputs, respectively. Lower bounds on the order of centralised and decentralised dynamic compensators for pole assignment are also established.