Stabilization of a Class of Switched Positive Nonlinear Systems

The problem of switching stabilization for a class of switched positive nonlinear systems (switched positive homogeneous cooperative system (SPHCS) in the continuous-time context and switched positive homogeneous order-preserving system (SPHOS) in the discrete-time context) is studied by using average dwell time (ADT) approach, where the positive subsystems are possibly all unstable. To tackle this problem, a new class of ADT switching is first defined, which is different from the previous defined ADT switching in the literature. Then, the proposed ADT is designed via analyzing the weighted l∞ norm of the considered system’s state. A sufficient condition of stabilization for SPHCSs with unstable positive subsystems is derived in continuous-time context. Furthermore, a sufficient condition for SPHOSs under the assumption that all modes are possibly unstable is also obtained. Finally, a numerical example is given to demonstrate the advantages and effectiveness of our developed results