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.