Linear systems of variable structure. Controllability and observability (Q5951241)

Linear, finite-dimensional, discrete-time control systems with constant coefficients are considered. The formal definitions of controllability, output controllability and observability are recalled. Next, using algebraic methods many conditions for controllability, output controllability and observability in a given finite time interval are formulated and proved. The duality property between controllability and observability is also discussed. Next, local controllability and local observability near the origin for the nonlinear control systems are considered. Finally the discrete Volterra control systems with variable structure are presented and discussed. Finally, some remarks and comments on controllability and observability of discrete-time systems are given. It should be mentioned that similar controllability, observability and duality problems for discrete-time control systems have been investigated in the reviewer's monograph [\textit{J. Klamka}, Controllability of dynamical systems. Dordrecht: Kluwer (1991; Zbl 0732.93008)].