【作者】 张竹青；

【导师】 吴保卫；

【作者基本信息】 陕西师范大学 ， 应用数学， 2005， 硕士

【摘要】 随着现代控制理论的研究日趋深入,以及它向其他学科如航空,航天,能源,网络,电力,石油,化工和通讯等应用领域的渗透,人们发现了一类更具广泛形式的动力系统,这就是奇异系统。奇异系统理论是20世纪70年代才开始形成并逐渐发展起来的现代控制理论的一个独立分支,它的模型存在于社会生产的诸多领域。因此,对奇异系统理论的研究具有深远的实际意义。 奇异系统与常规系统相互对应,既存在内在的联系又有本质的区别。但是到目前为止,奇异系统的研究思路大多是参照已有的常规系统理论向奇异系统推广和移植,其研究方法主要是状态空间方法,频率域方法和几何方法。本文用状态空间方法研究了奇异系统的极点配置问题;用频率域方法研究了奇异系统传递函数在虚轴二次型意义上的比较理论;用几何方法研究了奇异系统的干扰解耦问题。 本文得到的主要结论有: （1） 联合微分和比例输出反馈对奇异系统的极点配置。通过对奇异系统的系数矩阵作一种特殊的正交变换,给出了联合微分和比例输出反馈使变换后的奇异系统正则、无脉冲模且可极点配置的条件,并进一步研究了联合输出和状态反馈极点配置。即证明了存在微分和比例输出反馈（G,F）使奇异系统正则,无脉冲模且可对n₁个极点配置的充要条件是（ⅰ）E₃₃=0,E₅₅=0,A₃₃和A₅₅非奇异;（ⅱ）rank_ec=n₂+rankM;（ⅲ）m+p-1≥n₁。得到了在条件（ⅰ）（ⅱ）成立时,存在联合输出和状态反馈可对奇异系统n₁+n₂+n₄个极点进行配置。 （2） 奇异系统的传递函数在虚轴二次型意义上的比较理论。推广了常规系统的有界实引理,即根据常规系统的传递函数二次型意义上的比较理论,给出了奇异系统的传递函数在虚轴上的比较理论,并由其推出了奇异系统的有界实引理。所得的主要结论有:设系统（E,A,B,C,D）在C₀上无极点,且R>0,C₀表示虚轴,则下列命题等价: （ⅰ） （?）>0,s∈C₀。 （ⅱ） det（H（s））=0在虚轴无根。 （ⅲ） s∈C时,方程T₁（s）=T₃（s）Q（s）T₂（s）有一有理函数解Q（s）,使得当s∈C₀时,‖Q（s）‖<1,且此时T₃（s）的秩为p₃,T₂（s）的秩为m₂; 设系统（（?）,（?）,（?）,（?）,（?））在C₀无极点,且（?）>0,则下列命题等价: （ⅰ） T₂^*（s）T₂（s）>T₁^*（s）T₁（s）,s∈C₀。 （ⅱ） det（H_m（s））=0在虚轴无根。 （ⅲ） s∈C时,方程T₁（s）=Q（s）T₂（s）有一有理函数解Q（s）,使得当s∈C₀时,‖Q（s）‖<1,且T₂（s）的秩为m₂; 然后得到奇异系统的有界实引理形式:设奇异系统（（?）,（?）,（?）,（?））稳定,其中更多还原

【Abstract】 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更多还原