Convergence of switched linear systems with time-delay in detection of switching law

This study studies the stabilisation of second-order switched linear systems in which delays are present in detection of switching law. For stabilisable second-order switched linear systems and constant time-delay the authors find under which values of time-delay the switched system is stable under the same switching law. Hence, they prove the existence and uniqueness of a value of time-delay that satisfies that if time-delay is less, the system is stable and, if time-delay is greater, the system is not stable. Moreover, a method of estimating this value is obtained. Finally, a numerical example is presented in order to illustrate the results.