Hybrid system stability and robustness verification using linear matrix inequalities

By S. Pettersson, B. Lennartson. 2002

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Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results (2009, background): “Then the above matrix inequalities can be transformed into unconstrained ones based also on the -procedure, namely Theorem 13: [70]The system (1) is (exponentially) stable if there exist matrices and scalars , , , , and , such that”
Observer-based control of discrete-time Lipschitzian non-linear systems: application to one-link flexible joint robot (2005, background): “For more details on hybrid control and estimation of piecewise affine systems, the reader is referred to the following references (Ferrari-Trecate 2002, Cuzzola and Morari 2002, Balluchi et al. 2002, Pettersson and Lennartson 2002 and Li et al. 2003).”
Quadratic stabilizability of switched linear systems with polytopic uncertainties (2003, background): “The motivation for studying switched systems is from the fact that many practical systems are inherently multimodal in the sense that several dynamical subsystems are required to describe their behavior which may depend on various environmental factors (Dayawansa and Martin, 1999; Pettersson and Le”