.2-d System Strong To Control The Distance, The Balanced Model Reduction And Energy Uncoupling

Two-dimensional(2-D) linear systems has become an academic research area in recent years due to its importance in solving practical problem and its wide-ranged applications. A great number of notions and results in one-dimensional state-space systems have been extended to 2-D systems.In this thesis, basic research on qualitative theory and control of 2-D systems is performed. The content is divided into different categories shown as follow:a)The problem of controllability of 2-D Roesser model is studied .When the parameters of system are perturbed, the controllability of 2-D systems is discussed. A definition of the distance between controllable 2-D system and uncontrollable 2-D systems is given. And based on SVD, the bounds of the distance is presented.b)The problems of reachability and observability for 2-D continuous-discrete systems are studied. The realization which state elements are arranged according to the degree of reachability is obtained. The corresponding results of observability are obtained, too.c)A model reduction procedure of 2-D continuous-discrete systems, based on balanced state space representations, is studied.d)A method for decoupling multi-input multi-output 2-D discrete systems is presented. It is an approximate decoupling method, by which the energy of every input mainly controls the energy of a corresponding output and has little effect on the energy of the others. The results are obtained by LMIs so that the 2-D decoupling problem with stability is easy to be solved.