TABLE OF CONTENTS It has been demonstrated in Chapters 2 and 7 that the methods of equation error and regression can be used for estimation of parameters of the system if the measurements of states are available. This principle is extended to the output error method for parameter estimation to arrive at a method called the equation decoupling method, which is directly applicable for parameter estimation of unstable systems [4, 5]. In the equation decoupling method, the system state matrix is decoupled so that one part has only diagonal elements pertaining to each of the integrated states and the off-diagonal elements associated with the states use measured states in the state equations. Due to this, the state equations get decoupled. This decoupling of equations changes the unstable system to a stable one. Thus, it is clear that by incorporating stabilisation into the output error method by means of measured states, the instability caused due to numerical divergence of the integrated states can be overcome. Since the output error algorithm is stabilised by this method, these algorithms are termed stabilised output error methods. The degree of decoupling can be changed depending on the extent of instability in the system. This leads to two types of stabilised output error methods: i) equation decoupling when all the states pertaining to off-diagonal elements are replaced by corresponding measured states; and ii) regression analysis which results when only the states occurring with the parameters, which cause numerical divergence, are replaced by the...
