Proceedings ArticleDOI
Gramian based approach to model order-reduction for discrete-time switched linear systems
Abderazik Birouche,Jerome Guillet,Benjamin Mourllion,Michel Basset +3 more
- pp 1224-1229
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TLDR
The approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure, which helps to keep the biggest singular values of the system.Abstract:
This paper describes the problem of model orderreduction for a class of hybrid discrete-time switched linear systems composed of linear discrete-time invariant subsystems with a switching rule. The paper investigates a novel method to model reduction. The approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure. The error limit depends on the truncated singular values and balanced truncation procedure helps to keep the biggest singular values of the system. A numerical example shows the effectiveness of the proposed approach.read more
Citations
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Journal ArticleDOI
Balanced truncation for linear switched systems
TL;DR: A bound on the approximation error in the L2 norm for continuous-time and the l 2 norm for discrete-time linear switched systems is provided and it is shown that quadratic stability and LMI estimates of the L 2 and l 2 gains depend only on the input–output map.
Journal ArticleDOI
Data-Driven Model Order Reduction of Linear Switched Systems in the Loewner Framework
TL;DR: The Loewner framework for model reduction is extended to the class of linear switched systems and through this procedure, one can derive state-space models directly from data which is related to the input-output behavior of the original system.
Journal ArticleDOI
Model Reduction by Nice Selections for Linear Switched Systems
TL;DR: A moment-matching method for model reduction of linear switched systems (LSSs) is presented, which can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant systems.
Proceedings ArticleDOI
Model reduction by moment matching for linear switched systems
TL;DR: A moment-matching method for the model reduction of linear switched systems (LSSs) based upon a partial realization theory of LSSs and it is similar to the Krylov subspace methods used for moment matching for linear systems.
Journal ArticleDOI
Balanced truncation for linear switched systems
Ion Victor Gosea,Mihaly Petreczky,Athanasios C. Antoulas,Athanasios C. Antoulas,Athanasios C. Antoulas,Christophe Fiter +5 more
TL;DR: In this paper, a model order reduction approach for balanced truncation of linear switched-downloaded systems is proposed, where the authors compute pairs of controllability and observability Gramians corresponding to each discrete mode by solving systems of coupled Lyapunov equations.
References
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Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
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TL;DR: I. Stability under Arbitrary Switching, Systems not Stabilizable by Continuous Feedback, and Systems with Sensor or Actuator Constraints with Large Modeling Uncertainty.