Structured coprime factor model reduction based on LMIs

In this paper we discuss dynamic model reduction methods which preserve a certain structure in the underlying system. Specifically, we consider the situation where the reduction must be consistent with a partition of the system states. This is motivated, for instance, in situations where state variables are associated with the topology of a networked system, and the reduction should preserve this. We build on the observation that imposing block structure to generalized controllability and observability gramians automatically yields such state-partitioned model reduction. The difficulty lies in ensuring feasibility of the resulting Lyapunov inequalities, which is in general very restrictive. To overcome this, we consider coprime factor model reduction. We derive an LMI characterization of expansive and contractive coprime factorizations that preserve structure, and use this to build a more flexible method for structured model reduction. An example is given to illustrate the method. © 2004 Elsevier Ltd. All rights reserved

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 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 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

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

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

LMI relaxation to Riccati equations in structured ℋ<inf>2</inf> control

In this paper we discuss structured [image omitted] control methods for large-scale interconnected systems. Based on a relaxation of Riccati equations, we derive some linear matrix inequality (LMI) conditions for sub-optimal controllers in which information structure can be imposed. In particular, we derive controllers by solving low-dimensional LMIs, which are decentralized except for the sharing information between neighbours, as determined by the plant interconnection; also we optimize a performance bound for each of the derived controllers