Output feedback control for a class of nonlinear systems

Abstract

This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.

Robust output feedback control for a class of nonlinear systems with input unmodeled dynamics

“…Remark 1. The relation between (6) and (7) has been revealed in [5]. Here, a different proof above is given not only for completeness but also for getting the explicit relation between the constants γ and λ, which is useful for comparing the result in [4] with the one presented in this paper.…”

“…Assumption 2 [5] . The mappings fi(t, x) : R × R n → R, i = 1, 2, · · · , n are continuous, and there exists a constant γ > 0, such that for any s ∈ (0, 1), the inequality…”

“…For example, it is assumed that the nonlinear terms satisfy some global Lipshitz-like condition [3] , some triangular condition [2,4] , or some relaxed triangular condition which was presented in [5] recently.…”

“…However, the results in [5] did not consider the input unmodeled dynamics which are likely to appear in practical nonlinear systems. The control issue of nonlinear systems with input unmodeled dynamics was firstly stated by Kristic et al [6] It was shown that even in its simplest form, input unmodeled dynamics may result in dramatic shrinking of the region of attraction and finite escape time.…”

“…In short, the problem of input unmodeled dynamics commonly exists in practice, and is challenging. In this paper, we consider the robust global stabilization for a class of uncertain nonlinear systems with input unmodeled dynamics using output feedback, where the nonlinear terms satisfy a far more relaxed triangular condition as shown in [5], and the input unmodeled dynamics is assumed to be relative degree zero and minimum phase. A high gain dynamic output compensator is explicitly constructed to guarantee the globally asymptotic stability of the closed-loop system.…”