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2019 | OriginalPaper | Chapter

Estimates of the Minimal Eigenvalue of the Controllability Gramian for a System Containing a Small Parameter

Author : Mikhail Gusev

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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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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previous chapter Feedback Minimum Principle for Optimal Control Problems in Discrete-Time Systems and Its Applications

next chapter Optimality Conditions and Numerical Algorithms for Hybrid Control Systems

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Title: Estimates of the Minimal Eigenvalue of the Controllability Gramian for a System Containing a Small Parameter
Author: Mikhail Gusev
Publisher: Springer International Publishing
Book: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-22628-2

Electronic ISBN: 978-3-030-22629-9

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-22629-9_32

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