AN EXPLICIT ANALYSIS OF THE COVARIANCE SYSTEM IN A COVARIANCE ASSIGNMENT PROBLEM

Abstract

System analysis is essential in control theory. Stability, controllability and observability are vital issues to be considered in control systems. Different methods were used for the stability of linear systems. One of these methods is the Jury’s stability criterion used to ascertain the stability of discrete-time systems .This study investigates the stability of the corresponding covariance system of a Discrete-Time Linear Time-Invariant Stochastic Dynamical System (DTLTISDS) in a covariance assignment problem (CAP) via the Jury’s stability criterion. The characteristics equation was obtained from the transfer function of the covariance system. Necessary and sufficient conditions for stability was investigated utilizing the constant coefficients of resulting polynomial with respect to the characteristics equation and the Jury’s table .The Jury’s table was constructed with the aid of the constant coefficients of the polynomial and the Jury’s inner determinant methods. Kalman’s rank test was used to analyze controllability and observability. Results show that the covariance system is a stable system. The covariance system was also shown to be controllable and
observable