Abstract
We consider a linear time-invariant control system with right-hand side depending on a small parameter. Assuming that the system is controllable, we study the asymptotics of the minimal eigenvalue of a system’s controllability Gramian and provide some bounds for the eigenvalue. These estimates are applied to the study of convexity properties of reachable sets for nonlinear control systems with integral constraints on control variables.
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Gusev, M. (2019). Estimates of the Minimal Eigenvalue of the Controllability Gramian for a System Containing a Small Parameter. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_32
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DOI: https://doi.org/10.1007/978-3-030-22629-9_32
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