An infinite-time relaxation theorem for differential inclusions

By B. Ingalls, Eduardo Sontag, Yuan Yao Department of Mathematics, Rutgers University, Dept. of Mathematics, Florida Atlantic University. 2001

78 citations recorded by the source corpus.

The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wažewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/88a007b41b4cb9871a9aad179d7d26bbd056d394

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In Applied Mathematics

In Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

Analysis and synthesis of switched linear control systems (2005, background): “The following result is a special case of Theorem 1 in (Ingalls et al., 2003).”
Characterizations of input-to-state stability for hybrid systems (2009, background): “9], and [20, Corollary 1] (respectively, [19, Theorem 1 and Section III] and [9]).”
Review on computational methods for Lyapunov functions (2015, background): “often referred to as the Filippov-Wažewski Theorem, see also Ingalls, Sontag, and Wang 2002 [121].”
Monotone control systems (2002, unknown): “[18]).”
Input to State Stability: Basic Concepts and Results (2008, background): “The proof hinges upon a lemma given in [110], which may be interpreted ([41]) as a relaxation theorem for differential inclusions, relating global asymptotic stability of an inclusioṅ x ∈ F (x) to global asymptotic stability of its convexification.”