Study On Structural Analysis And Control Methods Of Generalized System

As is known to all, with the development of information technology and the modernization,people's requirements for modern control systems is also becoming higher and higher, however, the normal linear systems are increasingly unable to meet the current development of industry and information technology, so we must develop lots of derivatives of linear control systems to solve the problems which cannot be solved by normal linear systems. The generalized system is one of derivatives of linear control systems. On the basis of the generalized systems, in order to meet the actual needs, the generalized systems also gradually develop its own particularities which are consist of the property of time-delay,uncertainty,fault diagnosis and so on, so that the described power systems is more natural,more accurate, and more direct than the normal linear systems in responding to the nature of the things' law. It is the generalized systems' characteristics which are not owned by normal linear systems that are more meaningful.In this paper, the main content contains the stability analysis of the generalized systems and state feedback controller's design,and we divides into two different solutions for two different generalized systems here. For the complex and high dimensional generalized systems,we mainly use a limited equivalent transformation to simplify the systems'coefficient matrix in the algorithm and we can get the simplest form of generalized systems under normal circumstances. The main process is as follows: firstly, we make (E,A)convert into the simplest form by the equivalent transformation x(t) = Qx(t) and fix(E,A)and then simplify control input vector by an equivalent transformation u(t) = Qu(t) to achieve the finally simplified form. There are just one Jordan block, unit blocks and sub-block in the form of zero in simplified form(E, A) and it can ensure that the coefficient matrix of the derivative of state vector E is also a unit sub-block and a number of zero blocks, while its control input vector tries to simplify the form, too. Using the correlation of the state vector, high-dimensional matrix can be simplified into low-dimensional matrix.And some hidden features in the new system are easily to be found. It is one of the innovations of this article. While for the low dimensional generalized systems, here we mainly study a class of uncertain time-delay dependent switched generalized systems, using Lyapunov stability theory to analyze and prove the system quadratic stability and design its controller according to matrix norm and matrix inequalities, then we can obtain the boundary of the cost function,finally a numerical example is given to verify the correctness of the method.Finally,a summary of the full text and follow-up plans and prospects related content are given.