In this paper, the mathematical model of a kind of two-robot security system with an early warning function is studied. By using
strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the
system operator, the existence and uniqueness of nonnegative solution, and the well-posedness of solution are discussed, respectively.
Under the assumption that the failure rate and repair rate of the system are constants, the equations of the robot system
are transformed into an ordinary differential equation group, and then the instantaneous reliability and stable-state reliability of
the system are obtained. The reliability and zero-state controllability of the system are proved. Finally, the numerical solution of
the system model is obtained by using MATLAB mathematical software, and the corresponding numerical simulation diagram is
given. The results show that the conclusions of numerical calculation and numerical simulation are in accordance with the results
of reliability theory, thereby the reliability of the robot safety system is verified.
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