Robust and optimal control
Multidimensional Systems and Signal Processing
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Analysis of Second-Order Modes of Linear Discrete-Time Systems under Bounded-Real Transformations
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
| Hi-index | 0.00 |
This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.