Pole Assignment For Descriptor Systems Via Dynamic Compensators

System control theory is considered as one of subjects that occurring importantinfluence in human activities and social life. As an important part of system controltheory, descriptor system is developed as the need of science development as well asthe large-scale engineering techniques development. In the development, thepenetration of modern control theory and applications to other disciplines played animportant role. In this paper, as the research object to generalized lineartime-invariant systems, discussing pole assignment for descriptor system viadynamic compensators, the main results in the following two aspects:Firstly, for descriptor linear system with mutually exclusive poles, we discussthe problem of pole assignment for the system via proportional plus derivative statefeedback (i.e. dynamic order is zero) and the system via dynamic compensator (i.e.dynamic order is not zero). We propose the pole assignment methods forproportional plus derivative state feedback and dynamic compensator, presentsimple complete parametric solutions for eigenvectors of close-loop and coefficientmatrix of the controller. By selecting appropriate parameters, we can comfortablyget the solutions for the system via proportional plus derivative state feedback anddynamic compensator. For application of the singular value decomposition, themethod proposed in the paper is simple and having excellent numericalcharacteristics. Combined with specific example, we further demonstrate that theproposed method is simple and effective.Secondly, for descriptor linear system with multiple poles, we discuss theproblem of pole assignment for the system via dynamic compensator. We proposethe pole assignment method for the descriptor linear system with multiple poles,present simple complete parametric solutions for eigenvectors of close-loop andcoefficient matrix of the controller. By selecting appropriate parameters, we can getthe solutions for the problem of pole assignment for the system via dynamiccompensator. For application of the singular value decomposition, the methodproposed in the paper is simple and having excellent numerical characteristics.