AbstractThis paper investigates the ultimate boundedness of a linear system with a bounded uncertainty under some control input. These control inputs are determined so that the size of a bounded region, which ultimately the state of system reaches (the region of ultimate boundedness), is reduced. Then they are introduced as new control laws which are different from existing methods. These control laws consist of linear control laws for stabilizing a linear time‐invariant system, which is a basis for de signing, and modified control laws for making linear systems with disturbances, observation noises and uncertainty in system parameters, ultimately bounded. the control parameter contained in the latter modified control laws is determined so that the re gion of ultimate boundedness is reduced as much as possible by Lyapunov's second method. Control laws are linear when the control paprameter is a constant, and nonlinear when the parameter is a function of the state.In this paper, it is shown that the size of the region of ultimate boundedness obtained by the control laws newly proposed here is smaller than that obtained by the conventional Leitmann nonlinear control law.