Stability Criteria for Switched and Hybrid Systems

By Robert N. Shorten, Fabian R. Wirth, Oliver Mason, Kai Wulff, Christopher K. King. SIAM Review, 2007

1,098 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/153cdd1f5157ac76f0d499a8118c63808260de96

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Citations in the corpus

Positive recurrence of piecewise Ornstein–Uhlenbeck processes and common quadratic Lyapunov functions (2011, background): “As mentioned in the section on open problems of Shorten et al. (2007), it is of considerable interest to determine simple conditions for the existence of CQLFs. Theorem 1, which is our main technical contribution in this space, establishes such a result in the context of M-matrices and rank-1…”
Classical Converse Theorems in Lyapunov's Second Method (2015, methodology): “ete time version of the matrix conditions (17) was provided independently by Popov [85, Theorem 10.1.1] and Hitz 3The interested reader is directed to [112, Appendix H], [48, Section 10.1], [53], and [97]. 8 CHRISTOPHER M. KELLETT and Anderson [32] and is similar to the diﬀerence between the Lyapuno”
Review on computational methods for Lyapunov functions (2015, methodology): “Further good references for such methods are the book Boyd, Ghaoui, Feron, and Balakrishnan 1994 [42], the review Shorten, Wirth, Mason, Wulff, and King 2007 [206] and the review Sun 2010 [217].”
State feedback ℋ ∞ control design of continuous-time switched affine systems (2015, background): “The articles [11], [12] and [13] and the books [14] and [15] are surveys on this topic.”
Mather sets for sequences of matrices and applications to the study of joint spectral radii (2011, background): “In the past two decades discrete linear inclusions have attracted substantial interest in the control theory literature [1, 2, 16, 20, 24, 54, 56, 60].”
Stability Analysis of Positive Switched Linear Systems With Delays (2011, background): “[ 7 ] S. Tripakis, “Fault diagnosis for timed automata,” in Lecture Notes”
Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods (2010, background): “Impulsive systems are closely related to hybrid systems [1] and switched systems [2] and have wide range of applications.”