GENERATION OF LYAPUNOV FUNCTIONS FOR LINEAR TIME-INVARIANT SYSTEMS

Abstract

The direst method of Lyepunov is a general asthod which May be used to determine stability of sots of ordinary diffsrent iat equations • The main problem in this method is to find a systematic method to generate Lyapunov functions• At present• several methods are available, for this purpose• In the present thesis the method using phase, variable matrices and Routh*• or Schwarz+s canonical forms for the construe-tion of Lyapunov functions for Linear* time-invariant systems is discussed • This method requires proper transformation procedure to got the phase-'variable or canonical forms. The transformation techniques available at present have certain difficulties in their implementa-tion and Involve rather lengthy calculations • In this thesis new transformation techniques are proposed and discussed in details which are simple. elegant and yet general• Theass techniques involve far less work compared to the existing techniques. In particular It is shown that Routh' s and Schwarz • s canonical f oars can be easily written With the help of first column of Routh array• Further• a technique based on signal flow graph is also given which helps in the derivation of oompation matrix from a general state matrix. Some suggestion* for further r...arob work in order to extend these methods to tina'vary-ing ane non-t in+ar systems are Riven and it is bopad that the work in this direction w'i11 lead to more worthwhile r* suit ..