The Upper Bound of the Second-Order Modes of Linear State-Space Systems

Koshita, Shunsuke; Abe, Masahide; Kawamata, Masayuki

doi:10.1109/iscas.2005.1464751

Cited by 2 publications

(1 citation statement)

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“…We first introduce the following theorem that was derived in our previous work [12]. (11) and (12). Now, let (K P , W P ) and (K Q , W Q ) be the controllability and observability Gramians of (A, b, l, w) and (A, m, c, w), respectively.…”

Section: State-space Analysis Of Power Complementary Analog Filtersmentioning

confidence: 99%

State-Space Analysis of Power Complementary Analog Filters

Koshita

Abe

Kawamata

2007

2007 IEEE International Symposium on Circuits and Systems (ISCAS)

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Abstract-This paper presents a new analysis of power complementary analog filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. We show that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result means that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems.

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Section: State-space Analysis Of Power Complementary Analog Filtersmentioning

confidence: 99%