On Riccati Equations in Banach Algebras

Let R be a commutative complex Banach algebra with the involution ·⋆ and suppose that A ∈ Rn×n , B ∈ Rn×m , C ∈ Rp×n . The question of when the Riccati equation PBB⋆ P − PA − A⋆ P − C⋆ C = 0 has a solution P ∈ Rn×n is investigated. A counterexample to a previous result in the literature on this subject is given, followed by sufficient conditions on the data guaranteeing the existence of such a P. Finally, applications to spatially distributed systems are discussed.

• Type: Journal
• Year: 2011
• Where: SIAMCO
• Authors: Ruth Curtain, Amol Sasane
• Keywords: Commutative Complex Banach, Riccati Equation Pbb⋆, SIAMCO 2011, Software Engineering, Sufficient Conditions