Gramian based approach to model order-reduction for discrete-time switched linear systems

Birouche, Abderazik; Guillet, Jérôme; Mourllion, Benjamin; Basset, Michel

doi:10.1109/med.2010.5547881

Cited by 18 publications

(19 citation statements)

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“…A rich literature covers the subject of model reduction for switched systems, [6,7,8,9,10,11,12,13,14,15,16]. In particular, balanced truncation was explored in [1,2,14,13,15,12,16].…”

Section: Related Workmentioning

confidence: 99%

Balanced truncation for linear switched systems

Petreczky

Wiśniewski

Leth

2013

Nonlinear Analysis: Hybrid Systems

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In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems from [1,2]. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems [3]. Specifically in this paper, we provide a bound on the approximation error in L 2 norm for continuous-time and l 2 norm for discrete-time linear switched systems. We provide a system theoretic interpretation of grammians and their singular values. Furthermore, we show that the performance of balanced truncation depends only on the input-output map and not on the choice of the state-space representation. For a class of stable discrete-time linear switched systems (so called strongly stable systems), we define nice controllability and nice observability grammians, which are genuinely related to reachability and controllability of switched systems. In addition, we show that quadratic stability and LMI estimates of the L 2 and l 2 gains depend only on the input-output map.

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“…A rich literature covers the subject of model reduction for switched systems, [6,7,8,9,10,11,12,13,14,15,16]. In particular, balanced truncation was explored in [1,2,14,13,15,12,16].…”

Section: Related Workmentioning

confidence: 99%

Balanced truncation for linear switched systems

Petreczky

Wiśniewski

Leth

2013

Nonlinear Analysis: Hybrid Systems

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“…We have chosen a generalization of the classical balanced truncation method to LSS for comparison purposes. As opposed to most of the balancing methods we came across in the literature ( [11], [8], [36] and [33]), the method we choose (i.e [27]) does not require solving systems of LMI (linear matrix inequalities) which might be difficult for very large systems such as the one in Section 6.3. The results of the new proposed method turned out to be better than the ones obtained when using the BT method.…”

Section: Third Examplementioning

confidence: 99%

Data-Driven Model Order Reduction of Linear Switched Systems in the Loewner Framework

Gosea¹,

Petreczky²,

Antoulas³

2018

SIAM J. Sci. Comput.

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Abstract. The Loewner framework for model reduction is extended to the class of linear switched systems. One advantage of this framework is that it introduces a trade-off between accuracy and complexity. Moreover, through this procedure, one can derive state-space models directly from data which is related to the input-output behavior of the original system. Hence, another advantage of the framework is that it does not require the initial system matrices. More exactly, the data used in this framework consists in frequency domain samples of input-output mappings of the original system. The definition of generalized transfer functions for linear switched systems resembles the one for bilinear systems. A key role is played by the coupling matrices, which ensure the transition from one active mode to another. 1. Introduction. Model order reduction (MOR) seeks to transform large, complicated models of time dependent processes into smaller, simpler models that are nonetheless capable of accurately representing the behavior of the original process under a variety of operating conditions. The goal is an efficient, methodical strategy that yields a dynamical system evolving in a substantially lower dimension space (hence requiring far fewer computational resources for realization) yet retaining response characteristics close to the original system. Such reduced order models could be used as efficient surrogates for the original model, replacing it as a component in larger simulations.Hybrid systems are a class of nonlinear systems which result from the interaction of continuous time dynamical subsystems with discrete events. More precisely, a hybrid system is a collection of continuous time dynamical systems. The internal variable of each dynamical system is governed by a set of differential equations. Each of the separate continuous time systems is labeled as a discrete mode. The transitions between the discrete states may result in a jump in the continuous internal variable. Linear switched systems (LSSs) constitute a subclass of hybrid systems; the main property is that these systems switch among a finite number of linear subsystems. Also, the discrete events interacting with the subsystems are governed by a piecewise continuous function called the switching signal.Hybrid and switched systems are powerful models for distributed embedded sys-

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“…For discrete-time switched linear systems, see for instance [8] 1 Note that this class of systems is also referred to as Linear Switched Systems (or LSS) in the literature. and observability reduction with constrained switching, [17], [18], [38] for H ∞ -type reduction, and [16], [21], [33] for balancing-based methods. For continuous-time switched linear systems, see [6], [7], [22] for a class of moment-matching methods, [23], [27], [28], [32] for balancing-based methods and [31] for model reduction of systems affected by a lowrank switching.…”

Section: Introductionmentioning

confidence: 99%