Intrinsic difficulties in stochastic control of unstable convolution operators on Z

Stochastic control of causal, linear, unstable convolution operators on the full-time axis is shown to be impossible. The basic plant y = Gu and controller descriptions u = -Cy via possibly unstable convolution operators (or via their unstable transforms) have been shown to possess severe limitations in stochastic control studies on the full time axis Z and on Z(T). In fact, they have also similar limitations on N when G (or C) is noncausal and unstable (such situations can appear in applications in which the independent variable is a spatial variable rather than time).