Classes Of The Aggregation Problems Of Linear Singular System

Abstract: While the study of modern control theory developing gradually and impregnating into many application areas of aviation,spaceflight, energy sources, network, electric power, oil, chemical industry and communication etc, Scholars found a vast dynamic system, It is singular system.The theory of singular system started to form and gradually developed into a separate branch of modern control theory in the 1970s, Its models lies in many fields of social production. So,researching theory of singular system has far-reaching real significance.Singular system is corresponding to normal system.They have both internal logic and essential difference.But the study of singular system had mostly referred to the given normal system theory, which had been generalized and transplanted into singular system by far. The methods of study of singular system are mostly geometric approach,frequency domain method and state-space techniques.The paper studies pole placement of singular system by state-space techniques,then develops general statements for comparison of transfer functions of singular system in the sense of quadratic forms on the imaginary axis by frequency domain method and researches disturbance rejection in singular system by method of geometry.There are the main results:(1) Pole placement of singular system by derivative and proportional output feed-back.On the basis of special orthogonal transformation on singular system,We gives out the conditions that regulate the singular system by derivative and proportional output feedback into a new system which is not impulse modes and can be assigned poles.Moreover,The paper studies pole placement by state and output feedback.We prove the following: On the basis of orthogonal transformation on singular systems, the conditions that(i)E₃3 = 0, E₅5 = 0, A₃3 and A55 are nonsingular;(ii)rank_ec = n₂ + rankM; (iii)m + p -1 ≥ n1 are necessary and sufficient to regulate the singular system by derivative and proportional output feedback (G, F) into a closed-loop system which is not impulse modes and can be assigned n1 pole. Moreover, when condition (i)(ii) is satisfied, there is state and output feedback which can be assigned n1 + n2 + n4 poles.(2) The theory of comparison of transfer functions of singular system in the sense of quadratic forms on the imaginary axis. This paper generalized the bounded real lemma of normal system,and gives out comparison of transfer functions of singular system in the sense of quadratic forms,then obtained the bounded real lemma in the singular system. There are the main results: Assume that the singular system , A, B, C, D) has no pole on Co, and R > 0,then the following...