Stabilization of a Class of Switched Positive Nonlinear Systems

Abstract EN

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 switchedpositive homogeneous order-preserving system (SPHOS) in the discrete-time context) is studied by usingaverage dwell time (ADT) approach, where the positive subsystems are possibly all unstable.

To tacklethis problem, a new class of ADT switching is first defined, which is different from the previous definedADT 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 unstablepositive subsystems is derived in continuous-time context.

Furthermore, a sufficient condition for SPHOSsunder the assumption that all modes are possibly unstable is also obtained.

Finally, a numerical exampleis given to demonstrate the advantages and effectiveness of our developed results.