Positivity And Stability Analysis Of Descriptor Positive Linear Systems

Singular system also referred to as descriptor systems,generalized state-space systems,implicit systems,differential-algebraic systems,semi-state systems.The theoretical study began in 1970s and has now developed into an independent branch of modern control theory.The positivity and stability of positive singular systems are discussed in In this paper.The study of this paper mainly contains three parts:The first,for the singular positive linear discrete-time systems,a numerical method for judging positivity and stability of linear systems was given,which is based on the feasible solution of linear system of equations and linear programming.The method was presented by utilizing the straighten operator of matrix and minimal absolute difference.The second,for the singular positive linear continuous-time systems,a necessary and sufficient conditions for judging a Metzler matrix was first provided by the definition of Metzler matrix and Linear matrix nonnegativity constraints.Then,we give a new numerical method with linear programming to analysis the positivity for singular positive linear continuous-time system by bringing in Drazin inverse,straighten operator theorem of matrix and minimal absolute difference.The third,for the fractional positive linear discrete systems,the state space model was established by the simplistic fractional definition of Grunwald-Letnikov.Then the system description was transformed into linear positive discrete standard system by constructing a new state matrix.Next,a new numerical method for the system positivity and practical stability analysis was developed by applying the above-mentioned result.In this paper,the linear programming approach was applied to analysis the positivity and stability of the positive singular systems.The numerical method about positivity and stability of singular positive linear discrete-time systems,singular positive linear continuous-time system and fractional positive linear discrete systems.Then some numerical examples are given to validate the present results.Compared with the traditional results,the method of this paper is more simple and executable.It not only reduces the theory analysis complexity,but also improve the work efficiency.Finally,the main contents in the paper were summarized and the further research work were put forward.