A Control of Particular Poles of Linear Systems

摘要

In this work, the conditions under which the given poles of a linear stationary system can be moved to a required position, while the other poles strictly remain at their places, are justified. On the basis of stratification (decomposition) of the initial system, it is shown that to verify the solubility conditions of the problem, it is sufficient to compute a pair of matrices whose dimensions are defined by the number of poles to be corrected and to analyze the controllability of this pair. The structure of the set of controllers providing the control of the chosen poles is justified. The set of all controllers is analytically described for the special case of controlling one real pole. The technique is extended to the case when the invariance to external perturbations and the given placement of the system poles are provided simultaneously. The problem is solved on the basis of the matrix canonization method. An illustrative example is given.