PASSIVITY AND PASSIVATION OF FRACTIONAL-ORDER NONLINEAR SYSTEMS

Although the passivity of integer-order systems has been extensively analyzed, the research outcomes on the passivity of fractional-order nonlinear systems (FONSs) are scarce. This paper presents some theoretical results on passivity and passivation of FONSs. Based on the definition of the passivity of FONSs, and by using the Lyapunov stability theory and the linear matrix inequality (LMI) method, some conditions are derived to assure the FONSs is passive, which enrich the existing theoretical knowledge about the passivity of FONSs. Moreover, an observer-based output passive control is established to ensure that the corresponding closed-loop system is passive by means of LMI technique and matrix singular value decomposition (SVD). Ultimately, the practicality of our yielded results is revealed by two numerical simulations.

Automated summary

This paper presents theoretical results on the passivity and passivation of fractional-order nonlinear systems (FONSs), enriching the existing knowledge on the subject. Conditions are derived to ensure the passivity of FONSs, and an observer-based output passive control is established to guarantee the passivity of the corresponding closed-loop system. The practicality of the results is demonstrated through numerical simulations.