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Stability of Time Varying Linear Systems

  • Shashi K. Shrivastava
  • S. Pradeep
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 127)

Abstract

The concept of stability is one of the most fundamental in the study of natural sciences. The complexity of the stability problem depends on the degree of mathematical idealization of the system. In general, time invariant systems are much easier to handle than time varying systems. Here, first a bird’s eye view is presented on the important methods in constant parameter linear and nonlinear systems. Following this is a quick review of stability analysis of time varying systems touching upon periodic systems, second order systems, arbitrarily time varying systems, the absolute stability problem and the functional analytic approach. The paper also includes a summary of some important results of the authors’ work on the stability of second order multidimensional linear arbitrarily time varying systems. The theorems derived generalize some existing theorems. Application of one of them to the damped Mathieu equation yields better results than those existing in literature for some values in the parameter space. The asymptotic behaviour and boundedness of almost constant coefficient systems have also been studied and some new theorems derived.

Keywords

Time Invariant System Circle Criterion Time Vary Linear System Multiplier Criterion Large Space Structure 
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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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Shashi K. Shrivastava
    • 1
  • S. Pradeep
    • 1
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia

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