On (N + 1)-Tuple Riccati Stability

Source abstract

In this paper, we introduce the notion of tuple Riccati stability, which extends the classical concept of Riccati stability from a pair of matrices to an arbitrary finite collection of matrices. We establish an equivalent linear matrix inequality characterization and investigate several fundamental properties of the proposed notion, including hereditary, invariance, robustness, and convexity properties. As an application, we show that tuple Riccati stability provides a sufficient condition for the delay-independent asymptotic stability of linear systems with multiple constant delays by means of a Lyapunov–Krasovskii approach. We also establish a joint Schur–Cohn stability result that extends the classical spectral condition for Riccati-stable pairs to simultaneous combinations of multiple feedback matrices. Several consequences of this result are derived, illustrating how the proposed framework treats multiple feedback channels simultaneously. The results presented here generalize several well-known properties of classical Riccati stability and provide a unified framework for the analysis of systems with multiple delayed feedbacks.