In this paper, we study ℒ2 gain property for a class of switched systems which are composed of both continuous-time LTI subsystems and discrete-time LTI subsystems. Under the assumption that all subsystems are Hurwitz/Schur stable and have the ℒ2 gain less than 7, we discuss the ℒ2 gain that the switched system could achieve. First, we consider the case where a common Lyapunov function exists for all subsystems in ℒ2 sense, and show that the switched system has the ℒ2 gain less than the same level 7 under arbitrary switching. As an example in this case, we analyze switched symmetric systems and derive the common Lyapunov function clearly. Next, we use a piecewise Lyapunov function approach to study the case where no common Lyapunov function exists in ℒ2 sense, and show that the switched system achieves an ultimate (or weighted) ℒ2 gain under an average dwell time scheme.
|出版ステータス||Published - 2004 12 1|
|イベント||SICE Annual Conference 2004 - Sapporo, Japan|
継続期間: 2004 8 4 → 2004 8 6
|Conference||SICE Annual Conference 2004|
|Period||04/8/4 → 04/8/6|
ASJC Scopus subject areas
- コンピュータ サイエンスの応用