Error bounds in the gap metric for dissipative balanced approximations |
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Authors: | Chris Guiver Mark R Opmeer |
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Institution: | 1. Environment & Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, TR10 9EZ, United Kingdom;2. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom |
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Abstract: | We derive an error bound in the gap metric for positive real balanced truncation and positive real singular perturbation approximation. We prove these results by working in the context of dissipative driving-variable systems, as in behavioral and state/signal systems theory. In such a framework no prior distinction is made between inputs and outputs. Dissipativity preserving balanced truncation of dissipative driving-variable systems is addressed and a gap metric error bound is obtained. Bounded real and positive real input–state–output systems are manifestations of a dissipative driving-variable system through particular decompositions of the signal space. Under such decompositions the existing bounded real and positive real balanced truncation schemes can be seen as special cases of dissipative balanced truncation and the new positive real error bounds follow. |
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Keywords: | 93B11 93C05 15A24 46C20 47B50 |
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