Abstract
The finite-time stability (FTS) problem of uncertain neutral time-delay systems via a sliding mode control (SMC) approach is discussed in this paper. First, we construct a suitable sliding mode surface and an SMC law, which can guarantee the system states can reach the sliding mode surface in a finite time and maintain the sliding mode. Then, through the Lyapunov stability theory and the inequality techniques, the finite time stability of the closed-loop system during reaching phase and sliding mode phase is studied, a set of sufficient conditions which ensure the system to be finite-time stability is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the results.
Highlights
sliding mode control (SMC) is an effective nonlinear robust control method, which has strong robustness to resist parameter uncertainty and external disturbance of dynamical systems [1], [2]
finite-time stability (FTS) for uncertain systems over reaching phase and sliding motion phase were discussed in [21], [38]; the system in these papers is relatively simple. Different from these literatures, the neutral time-delay systems investigated in this paper have better universality, and the results can better reflect the quantitative relationship between the FTS conditions and the system parameters
We summarize the main contributions of this thesis: (a) Considering the effect of time delay and uncertainty, which makes our model have better universality; (b) The design method of sliding mode controller is given, which has good robustness to resist parameter uncertainty
Summary
SMC is an effective nonlinear robust control method, which has strong robustness to resist parameter uncertainty and external disturbance of dynamical systems [1], [2]. In [32], for a class of uncertain neutral delay systems with mismatched uncertainties, the author proposed a sliding mode control law to guarantee the asymptotic stability of closed-loop systems. Similar uncertain neutral time delay systems with SMC were studied in [32], [36], but these papers focused on the asymptotic stability of the system rather than FTS. FTS for uncertain systems over reaching phase and sliding motion phase were discussed in [21], [38]; the system in these papers is relatively simple Different from these literatures, the neutral time-delay systems investigated in this paper have better universality, and the results can better reflect the quantitative relationship between the FTS conditions and the system parameters. Asterisk(∗) means the term of symmetry. ∥ · ∥ denotes the Euclidean norm operator
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