Documentation |
Robust Control Toolbox™ software offers several algorithms for model approximation and order reduction. These algorithms let you control the absolute or relative approximation error, and are all based on the Hankel singular values of the system.
Robust control theory quantifies a system uncertainty as either additive or multiplicative types. These model reduction routines are also categorized into two groups: additive error and multiplicative error types. In other words, some model reduction routines produce a reduced-order model Gred of the original model G with a bound on the error $${\Vert G-Gred\Vert}_{\infty}$$, the peak gain across frequency. Others produce a reduced-order model with a bound on the relative error $${\Vert {G}^{-1}\left(G-Gred\right)\Vert}_{\infty}$$.
These theoretical bounds are based on the "tails" of the Hankel singular values of the model, i.e.,
$${\Vert G-Gred\Vert}_{\infty}\le 2{\displaystyle \sum _{k+1}^{n}{\sigma}_{i}}$$ | (3-1) |
where σ_{i} are denoted the ith Hankel singular value of the original system G.
$${\Vert {G}^{-1}\left(G-Gred\right)\Vert}_{\infty}\le {\displaystyle \prod _{k+1}^{n}\left(1+2{\sigma}_{i}\left(\sqrt{1+{\sigma}_{i}^{2}}+{\sigma}_{i}\right)\right)-1}$$ | (3-2) |
where σ_{i} are denoted the ith Hankel singular value of the phase matrix of the model G (see the bstmr reference page).
Top-Level Model Reduction Command
Method | Description |
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Main interface to model approximation algorithms |
Normalized Coprime Balanced Model Reduction Command
Method | Description |
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Normalized coprime balanced truncation |
Additive Error Model Reduction Commands
Method | Description |
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Square-root balanced model truncation | |
Schur balanced model truncation | |
Hankel minimum degree approximation |
Multiplicative Error Model Reduction Command
Method | Description |
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Balanced stochastic truncation |
Additional Model Reduction Tools
Method | Description |
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Modal realization and truncation | |
Slow and fast state decomposition | |
Stable and antistable state projection |