Positivization With Stability of Switched Linear Systems by Logic-Based Switchings

This letter investigates the positivization with the stability of switched linear systems by logic-based switchings without requiring the positivity conditions of each subsystem. First, the definitions on row submatrix and nonzero-row submatrix are introduced to characterize the structure of subsystems. Second, a logic-based switching law is designed based on the structural characteristics. Third, the sufficient conditions on the positivization together with stability for switched linear systems are derived in the framework of the logic switching law. Thus, based on the logic switching law, the sufficient conditions are presented for that of 3-D switched systems by further presenting a more concrete case. Finally, a numerical example is given to illustrate the validity of the proposed methods.