Stability Analysis of Discrete-Time Switched Positive Nonlinear Systems With Unstable Subsystems Under Different Switching Strategies

This note investigates the stability problem for discrete-time switched positive nonlinear systems (SPNSs) with unstable subsystems under different switching signals. Firstly, we propose the exponential stability criterion for a type of SPNSs when all subsystems succumb to average dwell time (ADT) switching by employing multiple Lyapunov functions (MLFs). The result obtained is then extended to switched positive linear systems (SPLSs). Moreover, the stability condition of SPNSs under a class of mode-dependent average dwell time (MDADT) switching is proposed, where all stable subsystems still follow the slow switching scheme, while all unstable subsystems obey the fast switching scheme, and the conclusion is also extended to SPLSs. Different from the existing results, a special Lyapunov function is constructed by virtue of the homogeneous of degree one and order-preserving properties of system functions in this brief. Finally, a simulation is furnished to validate the results obtained.