Dissipative Analysis And Control For Symmetric Systems

Symmetric system is a system with a special structure and widely used inthe dynamical system. Examples of such systems include circuit systems, elec-trical and power networks, structural systems, viscoelastic materials, chemicalreactions and so on. Dissipative theory plays an important role in the stabilityresearch of control systems since it was brought forward in 1970s. From theviewpoint of energy, a kind of analyze and design idea is put forward in thedissipative theory, which not only playing an important role in the controltheory aspect, but also in many real systems, such as robot systems, powersystems, chemical systems and so forth. In view of the extensive application indynamic systems, control theory and control engineering practice in the pastyears, symmetric system and dissipative theory have received considerable at-tention and made great progress.Based on the current research situation of symmetry system and dissi-pative theory, this thesis focuses on the problem of dissipative control androbust dissipative for linear symmetric systems, linear delayed symmetric sys-tems, linear descriptor symmetric systems. The main contents of the thesisare organized as follows:(1) The dissipative analysis and control problems for state-space symmet-ric system are discussed. Firstly, for state-space symmetric system, based onmatrix algebra tools and linear matrix inequalities, we give the necessary andsu?cient conditions for dissipative system and the explicit expression for dis-sipative index. Then, we consider the stabilization problems for state-spacesymmetric system and design a static output feedback controller such that theclosed-loop system be stable. The necessary and su?cient conditions for sta-bilization system and the range of controller are given. Last we consider thedissipative control problems for linear state-space symmetric system. Fromthe analysis results, the explicit expressions of dissipative index and gain of static output feedback controllers are given.(2) The dissipative analysis and control problems for state-space sym-metric time-delay system are investigated. At first, for state-space symmetricdelayed system, based on matrix algebra tools and linear matrix inequalities,we consider the dissipative analysis problems, stabilization problems and dis-sipative control problems. With regard to these problems, we give the explicitexpression of dissipative index and the parametric representation of staticoutput feedback controller gain. Then to the discrete time delay systems withstate-space symmetry, we obtain the similar results.(3) The dissipative analysis problems for state-space symmetric descriptorsystem are studied. we give an explicit expression of H∞norm computationfor continuous-time symmetric descriptor system and discrete-time symmetricdescriptor system respectively. The expressions only relate to the parametermatrix of descriptor systems and have advantages in computation.(4) The dissipative analysis and control problems for linear systems viaPI/PID controllers are considered. For linear time invariant systems, we designa PI controller which is similar to the static state feedback controller and aPI controller which is similar to the static output feedback controller anda PID controller which is similar to the dynamic output feedback controllerto investigate the dissipative control problems. On the basis of dissipativeanalysis and control results, we also discuss robust dissipative control problemsfor the linear time invariant systems with uncertainty, and give the parametricrepresentation for the PI/PID controller gains.In the thesis, the research objects consist of linear symmetric systems,linear time-delay symmetric systems, descriptor symmetric system and generallinear system. The methods and the conclusions are given more general.