ON SOME ASPECTS OF LINEAR TIME VARYING SYSTEMS

Abstract

The importance of state space analysis is recognised in fields where the time behaviour of any physical process is of interest. In state space approach the linear systems with time varying parameters can be .analyzed in more or less the - same manner as time-invariant linear systema. In this dissertation# the Chapter 1 is devoted to recognition of linear time-varyj,ng system and its presentation in state equations. Chapter 2 gives a detailed discussion of the forms, of response for various systems and their different properties. In Chapter 3 , the various methods to determine the linear time-varying system's solution in time domain are discussed including the most recent ones. Chapter 4 deals with the Lyapunov's first method as applied to time- varying linear systems and with some basic refinitiona of stability, while the Chapter 5 deals with aseertnining the stability by Lyapunov's second method , i.e. without actually solving the system. Finally the conclusions are drawn in Chapter 6 for a general analysis of linear time-varying systems.