2014/12/31 by J. Biemond, W.P.M.H. Heemels, Biemond, J. J. Benjamin +5
Engineering · #Adaptive Control of Nonlinear Systems #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1501.00161
openalex publication_date 2014/12/31 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The comparison between time-varying hybrid trajectories is crucial for\ntracking, observer design and synchronisation problems for hybrid systems with\nstate-triggered jumps. In this paper, a systematic way of designing an\nappropriate distance function is proposed that can be used for this purpose.\nThe so-called "peaking phenomenon", which occurs when using the Euclidean\ndistance to compare two hybrid trajectories, is circumvented by taking the\nhybrid nature of the system explicitly into account in the design of the\ndistance function. Based on the proposed distance function, we define the\nstability of a trajectory of a hybrid system with state-triggered jumps and\npresent sufficient Lyapunov-type conditions for stability of a hybrid\ntrajectory. A constructive design method for the distance function is presented\nfor hybrid systems with affine flow and jump maps and a jump set that is a\nhyperplane. For this case, the mentioned Lyapunov-type stability conditions can\nbe verified using linear matrix conditions. Finally, for this class of systems,\nwe present a tracking controller that asymptotically stabilises a given hybrid\nreference trajectory, and we illustrate our results with examples.\n