Linear Systems

  • Vladimir L. Kharitonov
Part of the Control Engineering book series (CONTRENGIN)


In this chapter we consider the class of neutral type linear systems with one delay. We define the fundamental matrix of such a system and present the Cauchy formula for the solution of an initial value problem. This formula is used to compute a quadratic functional with a given time derivative along the solutions of the time-delay system. It is demonstrated that this functional is defined by a special matrix valued function, which is called a Lyapunov matrix for a time-delay system. A thorough analysis of the basic properties of the matrix is included. Complete type functionals are introduced, and various applications of the functionals are discussed.


Exponential Stability Fundamental Matrix Exponential Estimate Neutral Type Special Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Vladimir L. Kharitonov
    • 1
  1. 1.Faculty of Applied Mathematics and Processes of ControlSaint Petersburg State UniversitySaint PetersburgRussia

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