Abstract
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 weightedl∞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.
Highlights
Switched system is a class of hybrid systems that involves a coupling between continuous dynamics and discrete events, which has wide application areas such as traffic control, process control, network control systems, automotive industry, and mechanical systems
We consider the problem of stabilization for switched positive nonlinear system (2) with our proposed average dwell time (ADT) switching
By Definition 7, we conclude that SPHCS (2) is globally uniformly exponentially stable (GUES) by our proposed ADT switching signals (3) satisfying (8) if the conditions (4)–(6) hold
Summary
Switched system is a class of hybrid systems that involves a coupling between continuous dynamics and discrete events, which has wide application areas such as traffic control, process control, network control systems, automotive industry, and mechanical systems. The authors of [24] presented a generalization of copositive types of Lyapunov function for stability analysis of switched positive systems Note that those works all consider switched positive linear systems. The existing time constrained switching stabilization results for switched positive systems are mainly focused on the linear case, and those promising ideas therein are not applicable for switched positive nonlinear systems. Such a problem becomes more complicated once all the nonlinear subsystems become unstable. X ⪰ y (or x ≻ y) mean that all entries of vector xi ≥ yi (or xi > yi)
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