Robustness of linear time‐invariant systems with feedback control protocols under random disturbances

Abstract In this paper, the robustness of global exponentially stable (ES) linear time‐invariant (LTI) systems with feedback control protocols is examined under the influence of random disturbances (RDs). For a given LTI system with global ES, a state feedback (SF) control protocol and a output feedback (OF) control protocol are proposed to keep the robustness of the discussed system, respectively. Meanwhile, how much the intensity of RDs that LTI system can withstand is obtained by the transcendental equation, in which the feedback gains are also designed and calculated by a proposed iterative algorithm. The theoretical analysis results demonstrate that the perturbed LTI systems may remain ES when the RDs are smaller than the upper bounds obtained in this paper. Finally, three cases are proposed to illustrate the effectiveness of the theoretical research.