Research On The Disturbance And Input-Output Simultaneous Decoupling For Multivariable Systems

The disturbance decoupling problem and input-output decoupling problem play a important role in classical as well as modern control theory. In this paper the disturbance and input-output simultaneous decoupling problem for multivariable systems is investigated extensively.Although the geometric approach and the structural approach have also been used to study this problem, and in principle these approachs can be used to verify the solvability of the problem, but they are complex and problematic. Moreover, they do not have numerically reliable and implementable algorithms.From what has been discussed above,in this paper the numerical computation of the disturbance and input-output simultaneous decoupling problem for linear time-invariant systems is considered using a condensed form and a matrix pencil approach .The condensed form is based on only orthogonal transformations, which can be implemented in a numerically stable way. Hence, an advantage of this approach is that the algorithms is numerically reliable and implementable.Moreover, the verification of the solvability conditions and the computation of the desired feedback matrices can be performed effectively using existing software tools such as LAPACK and Matlab.With decoupling problem for normal state space multivariable systems considered, the disturbance and input-output simultaneous decoupling problem for singular systems is studied also in this paper. The disturbance and input-output simultaneous decoupling problem for linear singular systems can be equal to the disturbance and input-output simultaneous decoupling problem for normal state space linear systems via equivalent transformations,which can simplify the promble.The equivalent relationship is established, and the suficient and necessary conditions are proved. So the disturbance and input-output simultaneous decoupling problem for linear singular systems can be solutioned by the result of normal state space multivariable systems.