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Nonlinear Control System Stability Metrics via A Singular Perturbation Approach

Yang, Xiaojing
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364466371

Abstract Details

2013, Doctor of Philosophy (PhD), Ohio University, Electrical Engineering (Engineering and Technology).
In this dissertation, Singular Perturbation Margin (SPM) and Generalized Gain Margin (GGM) are proposed as stability metrics for Linear Time-Invariant (LTI) systems, Linear Time-Varying (LTV) systems, Nonlinear Time-Invariant (NLTI) systems and Nonlinear Time-Varying (NLTV) systems, which are: (i) theoretically based, (ii) practically measurable, (iii) backward compatible in the sense that when applied to LTI systems, these metrics have a bijective correspondence with the Gain Margin (GM) and Phase Margin (PM). Based on eigenvalue perturbation theory, Lyapunov’s first and second methods, and algebraic spectral theory, the SPM and GGM assessment methods are established for LTI and LTV systems. The SPM and GGM equivalences between LTI and NLTI, LTV and NLTV systems are then established, which make it possible to estimate the SPM and GGM for NLTI and NLTV systems with the corresponding assessment methods for LTI and LTV systems, respectively. In the analysis and design of nonlinear systems, the determination of the Domain of Attraction (DOA) is a problem of fundamental importance, and through bifurcation analysis and Lyapunov’s methods, the relationship between the estimated DOA and the perturbation parameters are established. The concepts SPM, GGM and the corresponding assessment methods are helpful to analyze the advanced nonlinear and time-varying control techniques, thereby fully exploiting the performance potentials and improving the safety of the systems in the near future.
Jim Zhu (Committee Chair)
Douglas Lawrence (Committee Member)
222 p.
Electrical Engineering
Stability Margin; Nonlinear Systems; Singular Perturbation Approach; Regular Perturbation Approach; Stability Metrics

Recommended Citations

Citations

  • Yang, X. (2013). Nonlinear Control System Stability Metrics via A Singular Perturbation Approach [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364466371

    APA Style (7th edition)

  • Yang, Xiaojing. Nonlinear Control System Stability Metrics via A Singular Perturbation Approach. 2013. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364466371.

    MLA Style (8th edition)

  • Yang, Xiaojing. "Nonlinear Control System Stability Metrics via A Singular Perturbation Approach." Doctoral dissertation, Ohio University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364466371

    Chicago Manual of Style (17th edition)

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© 2013, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.