Ensuring of invariance of the output variables of linear systems to external unmatched disturbances under restrictions on the state variables and controls

The paper deals with the problem of ensuring of an invariance of the output variable of linear SISO system to external unmatched disturbances under restrictions on the state variables and control. External disturbances are assumed as unknown bounded in modulus functions of time. A mathematical model of control plant is represented in the canonical form of input-output. Smoothness requirements of external disturbances and the first derivative of given signal are absent. All state variables are measured. Under these assumptions the problem of state feedback design stabilizing tracking error with a given accuracy is solved within the block approach, the sliding mode theory and method of states space extension.