Abstract
The problem is considered here of decoupling the time-invariant multivariable dynamical system with m-inputs and r-outputs. First a necessary and sufficient condition for decoupling by the somewhat restricted state feedback law, u=GFx+Gω, is presented, together with a new algorithm for decoupling. Then the problem is extended to make it a decoupling problem by the general state feedback law, u=Fx+Gω. The algorithm derived for the restricted case is applied to establish a sufficient condition for decoupling the dynamical system by employing the general state feedback law. An algorithm is also given which allows us to obtain the decoupling pair (F, G) of the general state feedback law with a little addition of computational expense. A numerical example is included to illustrate the proposed algorithm. Finally it is shown that the stability of the decoupled system obtained by using such algorithm can be easily examined.
