Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On a boundary value problem of a class of generalized linear discrete-time systems | Dassios Advances in Difference Equations 2011 2011 51 http content 2011 1 51 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access On a boundary value problem of a class of generalized linear discrete-time systems loannis K Dassios Correspondence jdasios@. gr Department of Mathematics University of Athens Panepistimioupolis Athens Greece Springer Abstract In this article we study a boundary value problem of a class of generalized linear discrete-time systems whose coefficients are square constant matrices. By using matrix pencil theory we obtain formulas for the solutions and we give necessary and sufficient conditions for existence and uniqueness of solutions. Moreover we provide some numerical examples. These kinds of systems are inherent in many physical and engineering phenomena. Keywords linear difference equations boundary value problem matrix pencil discrete time system matrix difference equations 1 Introduction Linear matrix difference equations LMDEs are systems in which the variables take their values at instantaneous time points. Discrete time systems differ from continuous time ones in that their signals are in the form of sampled data. With the development of the digital computer the discrete time system theory plays an important role in control theory. In real systems the discrete time system often appears when it is the result of sampling the continuous-time system or when only discrete data are available for use. LMDEs are inherent in many physical engineering mechanical and financial actuarial models. In this article our purpose is to study the solutions of generalized linear discrete-time boundary value problems into the mainstream of matrix pencil theory. A boundary value problem consists of finding solutions which satisfies an ordinary matrix difference equation and appropriate boundary conditions at two or more points. Thus we consider FYk 1 GYk 1 with known boundary values
