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Stabilization of a linear system under control constraints is approached by combining the classical variation of parameters method for solving ODEs and a straightforward construction of a feedback law for the variational system based on a quadratic Lyapunov function. Sufficient conditions for global closed-loop stability under control constraints with zero in the interior and zero on the boundary of the control set are derived, and several examples are reported. The extension of the method to nonlinear systems with control constraints is described.
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Periodic event‐triggered control for incrementally quadratic nonlinear systems
Abstract Periodic event‐triggered control (PETC) evaluates triggering conditions only at periodic sampling times, based on which it is decided whether the controller needs to be updated. This article investigates the global stabilization of nonlinear systems that are affected by external disturbances under PETC mechanisms. Sufficient conditions are provided to ensure the resulting closed‐loop system is input‐to‐state stable (ISS) for the state feedback and the observer‐based output feedback configurations separately. The sampling period and the triggering functions are chosen such that the ISS‐Lyapunov function of continuous dynamics is also the ISS‐Lyapunov function of the overall system. Based on that, sufficient conditions in the form of linear matrix inequalities are provided for the PETC design of incrementally quadratic nonlinear systems. Two simulation examples are provided to illustrate the effectiveness of the proposed method.
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- Award ID(s):
- 1931744
- PAR ID:
- 10387546
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal of Robust and Nonlinear Control
- Volume:
- 31
- Issue:
- 11
- ISSN:
- 1049-8923
- Page Range / eLocation ID:
- p. 5261-5280
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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