The Property of the Second-Order Modes of Linear Discrete-Time Systems under Variable Transformation of Bounded-Real Function

摘要

This paper discusses the property of the second-order modes of discrete-time systems under variable transformation. Mullis and Roberts discovered that the second-order modes of discrete-time systems are invariant under variable transformation of any lossless bounded-real function, i.e. allpass function. This paper extends their theory to the case of the variable transformation of lossy function and reveals a novel property of the second-order modes under such variable transformation: it is proved that the values of the second-order modes are decreased under variable transformation of any lossy bounded-real function. The proof of this property is achieved with the help of the state-space representation of transformed discrete-time systems and the discrete-time bounded-real lemma.