The estimation of Linear Time Invariant (LTI) models is a standard procedure in System Identification. Any real-life system will however be nonlinear and time-varying, and the estimated model will converge to the LTI second order equivalent (LTI-SOE) of the true system. In this paper we consider some aspects of this convergence and the distance between the true system and its LTI-SOE. We show t...

We consider the design of three different control architectures for a step response tracking problem within a class of linear time-invariant (LTI) plants. Our goal is to motivate the use of a particular switching architecture that has been the subject of our prior work. We present the design of the particular switching architecture that we use and characterize its step response performance (mea...

The purpose of this paper is to describe a collection of test examples which can be used for testing and comparing algorithms for nonlinear semidefinite programs (NSDPs), bilinear matrix inequality (BMI) problems, (linear) control system design and related problems. COMPleib consists of examples collected from the engineering literature and real–life sources for linear time–invariant (LTI) cont...

It has recently been shown that a necessary and sufficient condition for the μstabilization of a linear time-invariant (LTI) retarded time-delay system by LTI decentralized finite-dimensional controllers is that the system should not have any μ-decentralized fixed modes with respect to decentralized static feedback. In the present work, we consider the stabilization of such systems by decentral...

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

In this paper we present an approach to test stability and feasibility of discrete-time LTI systems subject to constrained optimal control. The analysis is based on the feedback solution of the constrained optimal control problem formulated in a Receding Horizon fashion. The validation procedure consists of two independent parts. For stability, a piecewise quadratic Lyapunov function is compute...

We describe the use of the discrete wavelet transform (DWT) for system identification. Identification is achieved by using a test excitation to the system under test (SUT) that also acts as the analyzing function for the DWT of the SUT’s output, so as to recover the impulse response. The method uses as excitation any signal that gives an orthogonal inner product in the DWT at some step size (th...

Input design is an important issue for classical system identification methods but has not been investigated for the kernel-based regularization method (KRM) until very recently. In this paper, we consider in the time domain the input design problem of KRMs for LTI system identification. Different from the recent result, we adopt a Bayesian perspective and in particular make use of scalar measu...

This thesis considers two topics in the area of linear stochastic systems. The first topic is the construction of approximate finite dimensional linear time invariant (LTI) models for classical wide sense stationary stochastic signals with a non-coercive and non-rational spectral density, utilizing the recently developed theory of degree constrained rational interpolation. Non-coercive means th...