Piecewise Generalized Systems Linear Quadratic Control

The descriptor systems have attached much attention due to many areas in aerospace,energy,network,electric power,petroleum,chemical engineering and communication etc. Studying piecewise linear affine systems is an important branch of control theory, it mainly depends the partition of state space, carry on analysis to each linear district, then find the contact each others, which will bring out the whole properties of systems. In the last few years, along with the research of piecewise linear affine systems obtaining much progress, a lot of results on optimal control problems were obtained again. However, up to now, main research works are only limited to piecewise linear affine systems. Because descriptor systems have special properties, it is very difficulty to study optimal control of piecewise linear affine descriptor systems. Therefore, our research on the optimal control of piecewise linear affine descriptor systems have importance of actual meaning significance.This text gives analysises in detail research of piecewise linear (affine) systems in present, and emphasizes those about optimal control problems of piecewise linear affine descriptor systems. The main results include the following:(i) A brief summary of main results on piecewise linear systems is given.(ii) The problems of optimal control of piecewise linear affine descriptor systems are studied by using some elementary matrix transformations and line matrix inequalities. The estimates of upper and lower bounds of the optimal control are obtained.