Systems & Control Letters
A Tikhonov-type theorem for singularly perturbed differential inclusions
Nonlinear Analysis: Theory, Methods & Applications
Averaging of singularly perturbed systems
Nonlinear Analysis: Theory, Methods & Applications
On non-local stability properties of extremum seeking control
Automatica (Journal of IFAC)
Fast Switching Analysis of Linear Switched Systems Using Exponential Splitting
SIAM Journal on Control and Optimization
Smooth patchy control Lyapunov functions
Automatica (Journal of IFAC)
On singular perturbations due to fast actuators in hybrid control systems
Automatica (Journal of IFAC)
Averaging of nonsmooth systems using dither
Automatica (Journal of IFAC)
Solutions to hybrid inclusions via set and graphical convergence with stability theory applications
Automatica (Journal of IFAC)
Hi-index | 22.14 |
A class of singularly perturbed hybrid dynamical systems is analyzed. The fast states are restricted to a compact set a priori. The continuous-time boundary layer dynamics produce solutions that are assumed to generate a well-defined average vector field for the slow dynamics. This average, the projection of the jump map in the direction of the slow states, and flow and jump sets from the original dynamics define the reduced, or average, hybrid dynamical system. Assumptions about the average system lead to conclusions about the original, higher-dimensional system. For example, forward pre-completeness for the average system leads to a result on closeness of solutions between the original and average system on compact time domains. In addition, global asymptotic stability for the average system implies semiglobal, practical asymptotic stability for the original system. We give examples to illustrate the averaging concept and to relate it to classical singular perturbation results as well as to other singular perturbation results that have appeared recently for hybrid systems. We also use an example to show that our results can be used as an analysis tool to design hybrid feedbacks for continuous-time plants implemented by fast but continuous actuators.