Linear control systems

  • Jerzy Zabczyk
Part of the Systems & Control: Foundations & Applications book series (SCFA)


This chapter starts with basic results on semigroups of linear operators on Banach spaces. Characterizations of the generators of the semigroups due to Hille and Yosida and to Lions are given. Abstract material is illustrated by self-adjoint and differential operators. Non-homogeneous differential equations in Banach spaces, which are the mathematical models of infinite-dimensional control systems, are studied. Their weak and strong solutions are examined. The final sections are devoted to controlled delay equations: existence of solutions and the semigroup representations.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Jerzy Zabczyk
    • 1
  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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