Coprime factor model reduction for discrete-time uncertain systems

© 2014 Elsevier B.V. All rights reserved. This paper presents a contractive coprime factor model reduction approach for discrete-time uncertain systems of LFT form with norm bounded structured uncertainty. A systematic approach is proposed for coprime factorization and contractive coprime factorization of the underlying uncertain systems. The proposed coprime factor approach overcomes the robust stability restriction on the underlying systems which is required in the balanced truncation approach. Our method is based on the use of LMIs to construct the desired reduced dimension uncertain system model. Closed-loop robustness is discussed under additive coprime factor perturbations

Coprime factor model reduction for discrete-time uncertain systems

This paper presents a contractive coprime factor model reduction approach for discrete-time uncertain systems of LFT form with norm bounded structured uncertainty. A systematic approach is proposed for coprime factorization and contractive coprime factorization of the underlying uncertain systems. The proposed coprime factor approach overcomes the robust stability restriction on the underlying systems which is required in the balanced truncation approach. The method is based on the use of LMIs to construct the desired reduced dimension uncertain system model. ©2010 IEEE

Coprime factor model reduction for continuous-time uncertain systems

The paper considers the problem of coprime factor model reduction for a class of continuous-time uncertain systems with structured norm bounded uncertainty. The proposed method is applicable to the uncertain systems which may be robustly unstable, overcoming the robust stability restriction in the balanced truncation approach. A systematic approach is presented to construct a contractive coprime factor for the underlying uncertain system, based on the use of LMIs. This enables the balanced truncation to be applied to the contractive coprime factor to obtain the reduced uncertain system. Error bound on the L 2-induced norm of the resulting coprime factor is derived. © 2008 IEEE

A gramian-based approach to model reduction for uncertain systems

The technical note considers a problem of model reduction for a class of uncertain systems with structured norm bounded uncertainty. The technical note introduces controllability and observability Gramians in terms of certain parameterized algebraic Riccati inequalities. Based on these Gramians, three model reduction approaches are investigated for the underlying uncertain systems. © 2010 IEEE

Frequency-Weighted Model Reduction with Applications to Structured Models

In this paper, a frequency-weighted extension of a recently proposed model reduction method for linear systems is presented. The method uses convex optimization and can be used both with sample data and exact models. We also obtain bounds on the frequency-weighted error. The method is combined with a rank-minimization heuristic to approximate multiinput– multi-output systems.We also present two applications— environment compensation and simplification of interconnected models — where we argue the proposed methods are useful

Model reduction of behavioural systems

We consider model reduction of uncertain behavioural models. Machinery for gap-metric model reduction and multidimensional model reduction using linear matrix inequalities is extended to these behavioural models. The goal is a systematic method for reducing the complexity of uncertain components in hierarchically developed models which approximates the behavior of the full-order system. This paper focuses on component model reduction that preserves stability under interconnection

Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

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Reducing uncertain systems and behaviors

This paper considers the problem of reducing the dimension of a model for an uncertain system whilst bounding the resulting error. Model reduction methods with guaranteed upper error bounds have previously been established for uncertain systems described by a state-space type realization; specifically, by a linear fractional transformation (LFT) of a constant realization matrix over a structured uncertainty operator. In contrast to traditional 1-D model reduction where upper bounds on reduction are matched with comparable lower bounds, in the uncertain system problem there have previously been no lower bounds established. The computation of both upper and lower bounds is discussed in this paper, including a discussion of the use of Hankel-like matrices. These model reduction methods and error bound computations are then discussed in the context of kernel representations of behavioral uncertain systems