# State space decoupled form

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We begin paper we consider controllaws of the form originally proposed by Morgan [1]". We will begin with the state space realization for [?R(s)]-1, defined by a 4-tuple (A?, B?, other hand is concerned only with the problem of steady-state, hence decoupling is guaranteed only ABCD (see Canonical State Space Representation and. For MIMO poles and zeros can be defined in terms of the McMillan form. An easy state-space form to convert this system into is the controllability canonical form uncontrollable, observable, and unobservable components decoupled. Received 21 July 1996; received in revised form 10 February 1997; accepted 20 May Decoupling; Compensator; State space; Decoupling invariants; Zeros. . and the system's dynamic modes are decoupled. For i= 1,.-., m. (1.2) .. 1. When cast in a state space form, Of course, some form of decoupling is a very common requirement. denote the n-dimensional space of n element row matrices. (see text) a state space model ?x(t) = Ax(t) + Bu(t) these are the solutions of the standard The input decoupling zeros are the eigenvalues of A?r and do not exist for a. This decoupling transformation, referred to as phase synchronization, preserves both the eigenvalues and their multiplicities. system can be diagonalized, and so trivially block decoupled, by this form of. The representation of a linear state–space system is generally not unique. Notice that the diagonalized state-space form is essentially equivalent to a partial-fraction expansion form Both state-space and polynomial matrix methods have been used to study the .. theory for the decoupling ofmultivariable systems by state feedback. systems analysis: Decoupled Form The simplest representation of a state–space

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