A simple algebraic approach for stability analysis and certain schemes for model reduction of linear time invariant discrete

Abstract

In this thesis, a simple approach for stability analysis and three schemes for model reduction of the linear time-invariant discrete system are presented. The reduction schemes are extended to linear time-invariant continuous systems as well. A simple algebraic method for stability analysis is formulated by modifying the E.I. Jury table for discrete systems, in which new sufficient conditions for stability, sign criteria for number of roots lying outside, inside and on the unit circle are proposed. Singular cases are also dealt with comparatively easy procedure. The proposed approach has been extended to complex coefficient polynomials. Further this thesis is focussed on three different model reduction methods in which the scheme-1 has been developed from modified stability analysis table. For the linear time-invariant discrete systems, above mentioned modified E.I. Jury table is used to extract the reduced polynomials. The tables are developed for the numerator and denominator polynomials. Then the reduced order numerator and denominator polynomials are mined from the corresponding rows of the tables. The extracted model is adjusted with gain factor hence the steady state value has been maintained. For the linear timeinvariant continuous systems, fraction free Routh table which is developed by Bistritz is simplified and adopted to formulate the reduced order model. The illustrations show that the satisfactory results are produced by the proposed method. Scheme-2 is the amplitude matching technique developed for linear time-invariant discrete system, in which the amplitudes are chosen from step response plot of original higher order system and matched with the Laurentseries coefficients of unit step expression of reduced order function. The random choice of amplitudes from the plot may result in sample time mismatch. In such situation, sample time adjustment is implemented. The proposed scheme has been extended to continuous systems after the linear domain transformation which is suggested by Shamash. The formula