Controllability, Observability And Feedback Control Of 2-D Singular Systems

In this dissertation, the theory and methods of controllability, observability, characteristic polynomial assignment and optimal control of 2-D singular systems are investigated deeply and some contributions are made.Firstly, the response formula of Roesser model of 2-D singular systems is derived by the theory of two-dimensional Z transformation. Sufficient and necessary conditions for local reachability, local controllability and local observability in a rectangle of this model are presented. Using the properties of two-dimensional Z transformation, the equivalent definitions of local reachability, local controllability and local observability of Roesser model of 2-D singular systems are given. Accordingly, new sufficient and necessary conditions for local reachability, local controllability and local observability of this model are proposed.In addition, the algorithms of assigning the characteristic polynomial and finding the feedback gain matrix of 2-D system general model and 2-D singular Roesser model with single-input are investigated, respectively. They are also available for multi-input control systems with dyadic structure. In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment is transferred to the ones if a rational mapping is almost onto. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in Fornasini-Marchesini model II of 2-D systems via state feedback and output feedback are derived. Introducing the appreciate forms of state feedback and output feedback, the infinite poles of 2-D singular systems are eliminated. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of this model via state feedback and output feedback are given by the algebraic geometric method. The relation between the complex feedback and the real feedback is discussed. For 2-D systems and 2-D singular systems, it is shown that ifthere is a complex feedback to assign characteristic polynomial coefficients, then there exists a real feedback matrix to assign characteristic polynomial coefficients.Finally, with the response formula and some results of local reachability derived by two-dimensional Z transformation, the problem of minimum energy control of Roesser model of 2-D singular systems is solved. The problem of minimum energy control with bounded inputs is analyzed and the minimum energy control is obtained.