- Title
- Advances in stability analysis for nonlinear discrete-time dynamical systems
- Creator
- Tran, Duc Ngoc Anh
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2019
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- This thesis investigates stability analysis of discrete-time nonlinear dynamical systems. Stability, which plays a central role in nonlinear control system theory, has been studied extensively resulting in different frameworks such as l2-gain stability, Input-to-State stability (ISS), convergent dynamics, and contraction analysis. All of these frameworks were derived differently, were motivated distinctly, and employ different mathematical toolsets. As a consequence, their mutual relationships are, in general, not fully understood. For instance, the relationships between contraction analysis, incremental stability, and convergent dynamics are not clear although they all characterize asymptotically convergent behaviours between solutions of dynamical systems. Therefore, this thesis aims at three goals. First, we systematically review and propose stability and convergence properties for discrete-time systems that have been unavailable in the literature. Second, we thoroughly study qualitative relationships between important discrete-time stability and convergence notions. Third, we also present computational methods for certain bounds used in stability properties. We begin by reviewing stability properties for systems without inputs. We then study and propose Lyapunov function characterizations for so-called convergence properties: incremental stability, convergent dynamics, and contraction analysis. Subsequently, we demonstrate that convergent dynamics and incremental stability are two distinct properties. However, contraction analysis, which is distinctly different from convergent dynamics, is equivalent to a subset of incremental stability. For nonlinear systems with inputs, we begin by reviewing the classical ISS and input-output lp-gain stability properties and subsequently investigate two extensions of ISS: incremental ISS and ISS with respect to two measurement functions. We then examine relationships between ISS-based and lp-based properties. In particular, we demonstrate that, via nonlinear changes of coordinates, ISS and integral ISS are qualitatively equivalent to linear and nonlinear lp-gain properties, respectively. Illustrative examples with constructed changes of coordinates are provided to support the qualitative equivalence findings. Finally, we demonstrate two dynamic programming-based computational techniques including an extended real-valued terminal cost and a nonlinear "energy saturation" filter to estimate tight gain and transient bounds for the nonlinear l2-gain properties. Numerical examples are provided to showcase the application of the proposed computational methods.
- Subject
- input-to-state stability; discrete-time systems; nonlinear systems
- Identifier
- http://hdl.handle.net/1959.13/1405159
- Identifier
- uon:35450
- Rights
- Copyright 2019 Duc Ngoc Anh Tran
- Language
- eng
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|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 2 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 344 KB | Adobe Acrobat PDF | View Details Download |