Stability and convergence analysis for a class of nonlinear passive systems

Abstract

A systematic and general method that proves state boundedness and convergence to nonzero equilibrium for a class of nonlinear passive systems with constant external inputs is developed. First, making use of the method of linear-timevarying approximations, the boundedness of the nonlinear system states is proven. Next, taking advantage of the passivity property, it is proven that a suitable switching storage function can be always obtained to show convergence to the nonzero equilibrium by using LaSalle's Invariance Principle. Numerical and simulation results illustrate the proposed theoretical analysis.

Stability Analysis of DC Distribution Systems with Droop-Based Charge Sharing on Energy Storage Devices

“…Therefore, the complete stability proof and the sequence of the intermediate stages is as follows: (1) System (20) is examined for the input-to-state (ISS) stability property, since the ISS property implies BIBS stability [27,28]. The analysis follows Theorem A.1 [31] (Appendix B), and requires a suitable Lyapunov function to be analytically determined for the 11th-order closed-loop system; (2) In the second stage, the task is to prove convergence to a steady state equilibrium x * , different to zero, by applying the advanced analysis given in [32,33], and in particular Theorem A.2, under Assumptions A.1 and A.2, given in Appendix B, as well.…”

“…Additionally, since (22) holds true, system (20) is found to be strictly passive. As a result, assuming the external input to be constant or piecewise constant, and taking state boundedness and passivity into account, then Assumptions A.1 and A.2 and Theorem A.2 [32,33], as given in Appendix B, are satisfied. Hence, convergence to non-zero equilibrium is proven [32,33].…”

“…Basic Assumptions for convergence of a BIBS system [32,33]. Consider the nonlinear system: • For any trajectory x(t) ∈ Ω ⊂ R n , for all t ≥ 0 , the matrix A(x) is locally Lipchitz and Hurwitz.…”

Design and analysis of a novel bounded nonlinear controller for three-phase ac/dc converters

“…A contr (16) with A contr given by (11) Let the unforced closed-loop system (17), i.e. the system without the external input (u = 0):…”

“…Since, according to the analysis already discussed, system (22) is ISS, we can further apply Theorem 3 as given by the authors in [17] because all the other Assumptions mentioned in [17] are satisfied. Under these conditions, it becomes clear from [17] that there always exists a suitable storage function for system (22) with a constant external input u = Urn satisfying Theorem 3.…”