2024 |
Yutian Wang / Tengfei Liu / Hyungbo Shim / George A. Rovithakis / Zhong-Ping Jiang A Lyapunov Characterization of Prescribed Performance Control Systems Journal Article In: IEEE Transactions on Automatic Control, vol. 69, iss. 11, pp. 7917 - 7924, 2024, ISSN: 0018-9286. Abstract | Links | BibTeX | Tags: Input-to-state practical stability, Lyapunov function, Prescribed performance control @article{nokey, This paper contributes a Lyapunov formulation for prescribed performance controller designs. In particular, we first show that the closed-loop system of a typical class of prescribed performance control systems can be transformed into an interconnection of input-to-state practically stable (ISpS) subsystems characterized by ISpS-Lyapunov functions. Then, we take advantage of the gain-interconnections between the subsystems and construct a Lyapunov function for the closed-loop system. The proposed approach is validated through prescribed performance control for both SISO and MIMO plants, as well as systems not necessarily in the lower-triangular form and systems with dynamic uncertainty. |
2023 |
Hiroshi Ito / Hyungbo Shim A Toolkit for Globally Robust Observer-Based Feedback with Relaxed Characterization of iISS/ISS Journal Article In: IEEE Transactions on Automatic Control, vol. 68, iss. 7, pp. 3858-3871, 2023, ISSN: 0018-9286. Abstract | Links | BibTeX | Tags: Integral input-to-state stability, Lyapunov function, Output feedback, Small gain theorem @article{nokey, This paper elaborates on flexibility in dealing with the interconnection of integral input-to-state stable (iISS) and input-to-state stable (ISS) systems. The undecoupled characterizations introduced separately for iISS and ISS in the literature are linked to build a framework enabling global analysis without settling for local and semi-global properties. Feedback control design in the presence of measurement noise can benefit from the framework immediately if plants are nonlinear, irrespective of application areas. This paper proposes a toolkit for providing robustness guarantees in observer-based output feedback control subject to measurement noise. For a nonlinear plant, the couplings among the plant state, the estimation error, and the measurement noise arising in the closed-loop equations often hinder global analysis such as ISS with respect to the measurement noise. In the formalism of iISS, this paper demonstrates that the flexibility in dealing with the couplings allows one to establish the robustness globally. Moreover, it gives a condition under which the closed-loop system can possess ISS and strong iISS which are stronger than iISS. |
2021 |
Aneel Tawani / Hyungbo Shim Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics Proceedings Article In: Proc. of 2021 IEEE 60th Conference on Decision and Control, pp. 5382-5387, IEEE, Austin, Texas, USA, 2021. Abstract | Links | BibTeX | Tags: Hybrid system, Lyapunov function, Singular perturbation @inproceedings{nokey, This article considers the stability analysis for a class of hybrid systems with the focus being on the frequently occurring jump dynamics. The system class is modelled as a singularly perturbed hybrid system where the singular perturbation parameter governs the frequency of jumps. Consequently, this results in a quasi steady-state system modeled by a differential equation without any jumps, and the boundary-layer system described by purely discrete dynamics. By imposing appropriate assumptions on the quasi steady-state system and the boundary-layer system, we derive results showing practical convergence to a compact attractor when the jumps occur frequently often. Our system class is motivated by the control design problem in a network of second-order continuous-time coupled oscillators, where each agent communicates the information about its position to the neighbors at discrete times. As a corollary to our main result, we show that if the information exchange between the agents and their neighbors is frequent enough, then the oscillators achieve practical consensus. |
2001 |
Hyungbo Shim / Daejong Noh / Jin Heon Seo Common Lyapunov function for exponentially stable nonlinear systems Proceedings Article In: Proc. of 4th SIAM Conference on Control and Its Applications, SIAM SIAM, 2001. Abstract | Links | BibTeX | Tags: Lyapunov function @inproceedings{ShimNhoSeo01, We present a sufficient condition for the existence of a common Lyapunov function for a family of exponentially stable nonlinear systems. Suppose that there are m systems ˙x = fi(x) each of which is exponentially stable. When any pair of the vector fields fi(x) are commuting, i.e. the Lie bracket of the pair is zero, there is one Lyapunov function V (x) which guarantees the exponential stability for all of them. |
List of English Publication
2024 |
A Lyapunov Characterization of Prescribed Performance Control Systems Journal Article In: IEEE Transactions on Automatic Control, vol. 69, iss. 11, pp. 7917 - 7924, 2024, ISSN: 0018-9286. |
2023 |
A Toolkit for Globally Robust Observer-Based Feedback with Relaxed Characterization of iISS/ISS Journal Article In: IEEE Transactions on Automatic Control, vol. 68, iss. 7, pp. 3858-3871, 2023, ISSN: 0018-9286. |
2021 |
Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics Proceedings Article In: Proc. of 2021 IEEE 60th Conference on Decision and Control, pp. 5382-5387, IEEE, Austin, Texas, USA, 2021. |
2001 |
Common Lyapunov function for exponentially stable nonlinear systems Proceedings Article In: Proc. of 4th SIAM Conference on Control and Its Applications, SIAM SIAM, 2001. |