
Accession Number : ADA195645
Title : Stability, Stochastic Stationarity and Generalized Lyapunov Equations for TwoPoint BoundaryValue Descriptor Systems,
Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
Personal Author(s) : Nikoukhah, Ramine ; Levy, Bernard C ; Willsky, Alan S
PDF Url : ADA195645
Report Date : 03 Mar 1988
Pagination or Media Count : 52
Abstract : This paper introduces the concept of internal stability for twopoint boundaryvalue descriptor systems (TPBVDSs). Since TPBVDSs are defined only over a finite interval, the concept of stability is not easy to formulate for these systems. The definition which is used here consists in requiring that as the length of the interval of definition increases, the effect of boundary conditions on states located close to the center of the interval should go to zero. Stochastic TPBVDSs are studied, and the property of stochastic stationarity is characterized in terms of a generalized Lyapunov equation satisfied by the variance of the boundary vector. A second generalized Lyapunov equation satisfied by state variance of a stochastically stationary TPBVDS is also introduced, and the existence and uniqueness of positive definite solutions to this equation is then used to characterize the property of internal stability. Keywords: Stability, Twopoint boundary value problems. (hde)
Descriptors : *BOUNDARY VALUE PROBLEMS, *LYAPUNOV FUNCTIONS, EQUATIONS, INTERNAL, INTERVALS, LENGTH, STABILITY, VARIATIONS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE