This paper discusses the problem of constraints on both control and its increment for linear systems in state space form, in both the continuous and discrete time domains. For autonomous linear systems with constrained increment, necessary and sufficient conditions are derived, such that the evolution of the system respects the incremental constraints. It is also derived a pole placement technique to solve inverse problem, deriving stabilizing state feedback controllers which respect constraints on both control and its increment. An illustrative example shows the application of the method.