Book ; Online: Converse negative imaginary theorems
2023
Abstract: Converse negative imaginary theorems for linear time-invariant systems are derived. In particular, we provide necessary and sufficient conditions for a feedback system to be robustly stable against various types of negative imaginary (NI) uncertainty. ... ...
Abstract | Converse negative imaginary theorems for linear time-invariant systems are derived. In particular, we provide necessary and sufficient conditions for a feedback system to be robustly stable against various types of negative imaginary (NI) uncertainty. Both marginally stable and exponentially stable uncertain NI systems with restrictions on their static or instantaneous gains are considered. It is shown that robust stability against the former class entails the well-known strict NI property, whereas the latter class entails a new type of output strict NI property that is hitherto unexplored. We also establish a non-existence result that no stable system can robustly stabilise all marginally stable NI uncertainty, thereby showing that the uncertainty class of NI systems is too large as far as robust feedback stability is concerned, thus justifying the consideration of subclasses of NI systems with constrained static or instantaneous gains. Comment: This paper has been submitted for possible publication at Automatica |
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Keywords | Electrical Engineering and Systems Science - Systems and Control ; Mathematics - Optimization and Control |
Subject code | 515 |
Publishing date | 2023-06-03 |
Publishing country | us |
Document type | Book ; Online |
Database | BASE - Bielefeld Academic Search Engine (life sciences selection) |
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