Weighting patterns and the controllability and observability of time-variable 2D continuous-discrete linear systems (Q2770042)

Linear, finite-dimensional, continuous-discrete 2D control systems with variable coefficients are investigated. Using an appropriately defined state transition matrix and the discrete-time fundamental matrix, the exact form for the solution for given initial and boundary conditions is presented. Next, using algebraic methods, necessary and sufficient conditions for controllability and observability in a given domain are formulated and proved. These conditions have the rank conditions form and are a generalization to the continuous-discrete case of the familiar controllability and observability conditions for continuous or discrete control systems.NEWLINENEWLINENEWLINEIt should be mentioned that similar controllability and observability considerations can be found in [\textit{J. Klamka}, Controllability of 2D continuous-discrete abstract linear systems, Proc. European Control Conference ECC'95, Roma, 5-8.09.1995, Vol. 3, 2208-2213 (1995)] and \textit{T. Kaczorek}, Positive 1D and 2D systems, Springer-Verlag, Berlin (2002; Zbl 1005.68175)]. Moreover, the weighting pattern is defined, and the connection to the minimality of a realization and its controllability and observability is discussed.