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Equilibrium Points of Linear Systems with Single Saturated Input Under Commuting Conditions

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Stability and Control of Nonlinear Time-varying Systems

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Abstract

In this chapter, commutative matrices of multiple-input multiple-output (MIMO) linear systems are considered. The existence of the feedback matrices of a commutative state matrix set in the MIMO closed loops is reduced to the existence of an invariant subspace of a matrix A. The existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by Kronecker products. By defining new equilibrium points, the relationship between equilibrium points is discussed for a linear system with a single saturated input. Four criteria for equilibrium points are outlined for such linear systems. Finally, four interesting examples, including their corresponding simulation plots, are shown to illustrate the above results.

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Acknowledgements

This work is Supported by National Key Research and Development Program of China (2017YFF0207400).

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Authors and Affiliations

  1. Key Laboratory of Complex System Intelligent Control and Decision, School of Automation, Beijing Institute of Technology, Beijing, China

    Shuli Guo

  2. Department of Cardiovascular Internal Medicine of Nanlou Branch, National Clinical Research Center for Geriatric Diseases, Chinese PLA General Hospital, Beijing, China

    Lina Han

Authors
  1. Shuli Guo
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  2. Lina Han
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Correspondence to Shuli Guo .

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Guo, S., Han, L. (2018). Equilibrium Points of Linear Systems with Single Saturated Input Under Commuting Conditions. In: Stability and Control of Nonlinear Time-varying Systems. Springer, Singapore. https://doi.org/10.1007/978-981-10-8908-4_2

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  • DOI: https://doi.org/10.1007/978-981-10-8908-4_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8907-7

  • Online ISBN: 978-981-10-8908-4

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