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

  • Shuli Guo
  • Lina Han


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.



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


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Key Laboratory of Complex System Intelligent Control and Decision, School of AutomationBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Cardiovascular Internal Medicine of Nanlou Branch, National Clinical Research Center for Geriatric DiseasesChinese PLA General HospitalBeijingChina

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