Non-linear impulsive dynamical systems. Part I: Stability and dissipativity

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Robust H∞ control of uncertain linear impulsive stochastic systems (2008, unknown): “In addition, for linear impulsive systems, the proposed results in [9] provide a generalization of the positive real lemma and the bounded real lemma.”
PASSIVITY AND PASSIVITY BASED CONTROLLER DESIGN OF A CLASS OF SWITCHED CONTROL SYSTEMS (2005, background): “For switched control systems, at present, there are very few results available that deal with the subject in hybrid systems (Haddad et al., 2001), (Pogromsky et al., 1998), and (Zefran et al., 2001).”
Dissipativity Theory for Switched Systems (2005, methodology): “Dissipativity and stability analysis for general impulsive and hybrid systems were addressed in [8] and [9], where necessary and sufficient conditions for dissipativity using a common storage function”
Non-linear impulsive dynamical systems. Part II: Stability of feedback interconnections and optimality (2001, methodology): “Proof: Local and global asymptotic stability is a direct consequence of (42) and (43) by applying Theorem 2 of Haddad et al. (2001) to the closed-loop system (39), (40).”