Computation of the Inner-outer Factorization for Time-varying Systems
نویسنده
چکیده
An inner-outer factorization theorem for linear time-varying systems is obtained via an extension of the classical Beurling-Lax theorem to the time-varying context. This provides characteristic features of the inner factor, which can be used to compute realizations of the inner and outer factors from a realization of the given transfer operator. The resulting algorithm is unidirectional in time. The outer factor can also be obtained by an expression involving a Riccati recursive equation.
منابع مشابه
On Spectral Factorization and Riccati Equations for Time-Varying Systems in Discrete Time
It is known that positive operators Ω on a Hilbert space admit a factorization of the form Ω = W∗W, where W is an outer operator whose matrix representation is upper. As upper Hilbert space operators have an interpretation of transfer operators of linear time-varying systems in discrete time, this proves the existence of a spectral factorization for time-varying systems. In this paper, the abov...
متن کاملComputation of general inner-outer and spectral factorizations
In this paper we solve two problems in linear systems theory: the computation of the inner–outer and spectral factorizations of a continuous–time system considered in the most general setting. We show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic Riccati equation of order usually much smaller than the McMillan degree of the trans...
متن کاملExact Elasticity Solutions for Thick-Walled FG Spherical Pressure Vessels with Linearly and Exponentially Varying Properties
In this paper, exact closed-form solutions for displacement and stress components of thick-walled functionally graded (FG) spherical pressure vessels are presented. To this aim, linear variation of properties, as an important case of the known power-law function model is used to describe the FG material distribution in thickness direction. Unlike the pervious studies, the vessels can have arbit...
متن کاملADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH UNKNOWN DISTRIBUTED TIME-VARYING DELAYS AND UNKNOWN CONTROL DIRECTIONS
In this paper, an adaptive fuzzy control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the control gains.Based on the backstepping technique, the adaptive fuzzy controller is constructed. The main contributions of the paper...
متن کاملFrequency Aanalysis of Annular Plates Having a Small Core and Guided Edges at Both Inner and Outer Boundaries
This paper deals with frequency analysis of annular plates having a small core and guided edges at both inner and outer boundaries. Using classical plate theory the governing differential equation of motion for the annular plate having a small core is derived and solved for the case of plate being guided at inner and outer edge boundaries. The fundamental frequencies for the first six modes of ...
متن کامل