In this paper, we study the passive problem of uncertain fractional-order neural networks (UFONNs) with time-varying delays. First, we give a sufficient condition for the asymptotic stability of UFONNs with bounded time-varying delays by using the fractional-order Razumikhin theorem. Secondly, according to the above stability criteria and some properties of fractional-order calculus, a delay-dependent condition that can guarantee the passivity of UFONNs with time-varying delays is given in the form of a linear matrix inequality (LMI) that can be reasonably solved in polynomial time using the LMI Control Toolbox. These conditions are not only delay-dependent but also order-dependent, and less conservative than some existing work. Finally, the rationality of the research results is proved by simulation.
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.
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