Observability of Discrete-Time Linear Systems with Communication Protocols and Dropouts

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Data Driven Stability Analysis of Black-box Switched Linear Systems

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius

Path-complete p-dominant switching linear systems

The notion of path-complete p-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratic cones in the state space. We show that path-dominant systems have a low-dimensional dominant behavior, and hence allow for a simplified analysis of their dynamics. An algorithm for deciding the path-dominance of a given system is presented

Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirement