Study of Stabilising Strategies for Switched Linear Systems

The stabilisability problem of a class of single-input switched linear systems is considered. The dimension of the system is reduced with the variable-structure control. The sufficient conditions of the uniform stabilisation of the systems and the existence of the admissible stabilising strategies of the systems are obtained through the study of the sliding mode of the reduced systems. And the detailed admissible stabilising strategy sets are proposed. The completely admissible stabilising strategies for second-order switched systems are given as an application. Some numerical simulations validate the main results.