Balanced Truncation of Stable Discrete Time Second-Orderly Structured Systems

Abstract

Mathematical modeling is the only depiction of the physical systems in literary world. But
due to complexity, these models are to be expressed in equivalently curtailed models. Framework for sundry
non-existent techniques for order curtailment of stable discrete time second-orderly structured systems
(SOSs) are suggested in this manuscript. Discrete SOSS is transmuted into generalized configuration
and discrete time algebraic Lyapunov equations (DALEs) are composed. Gramians for balancing are
procured from DALEs. Fragmentation of gramians into position and velocity snippets is of utmost
importance. Once fragmentation takes place, structure retention in ROM is procured and balanced
curtailment is solicited. Sundry versions of balanced transformations are introduced. Position and velocity
gramians are balanced in disparate combinations. Balanced truncation based on magnitude of Hankel
singular values is established to procure the reduced order model that veraciously depict the incipient
system. As suggested contrivance hangs on to secondorderly structure and carries dynamics of stabilized
system therefore, this contrivance truely surmises original system behavior. Numerical results are
incorporated to ratify the suggested mechanism.