2024 |
Sihyun Ahn / Hyungbo Shim / Daniel Liberzon Semi-global practical stability of nonlinear systems with slow and fast time variation and switching in a separable form Proceedings Article In: 2024 IFAC Conference on Analysis and Control of Nonlinear Dynamics and Chaos, 2024. Abstract | BibTeX | Tags: Lyapunov method, Switched systems @inproceedings{nokey, This paper investigates stability of nonlinear systems, which has the separable form, with time-varying parameters. When the parameters are frozen, the system is stable, and the stability question is for the case when the parameters are fast-varying but its (time-varying) average (defined in a certain sense) varies slowly. Here, we allow the slowly-varying average to be discontinuous as long as its total variation has small growth. While existing results are based on the assumption that the equilibrium is invariant with respect to the parameters, we extend them to the case where the equilibrium is invariant with respect to the average of the fast-varying parameters. |
2016 |
Hyungbo Shim / Daniel Liberzon Nonlinear Observers Robust to Measurement Disturbances in an ISS Sense Journal Article In: IEEE Transactions on Automatic Control, vol. 61, no. 1, pp. 48-91, 2016. Abstract | Links | BibTeX | Tags: Control system synthesis, Lyapunov method @article{ShimLiberzon16, This paper formulates and studies the concept of quasi-Disturbance-to-Error Stability (qDES) which characterizes robustness of a nonlinear observer to an output measurement disturbance. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant's input and state remain bounded. We develop Lyapunov-based sufficient conditions for checking the qDES property for both full-order and reduced-order observers. We use these conditions to show that several well-known observer designs yield qDES observers, while some others do not. Our results also enable the design of novel qDES observers, as we demonstrate with examples. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an application of this idea, we treat a problem of stabilization by quantized output feedback. |
List of English Publication
2024 |
Semi-global practical stability of nonlinear systems with slow and fast time variation and switching in a separable form Proceedings Article In: 2024 IFAC Conference on Analysis and Control of Nonlinear Dynamics and Chaos, 2024. |
2016 |
Nonlinear Observers Robust to Measurement Disturbances in an ISS Sense Journal Article In: IEEE Transactions on Automatic Control, vol. 61, no. 1, pp. 48-91, 2016. |