Group and total dissipativity and stability of multi-equilibria hybrid automata

• Main Authors: Navarro-Lopez, Eva Maria (Author), Laila, Dina Shona (Author)
• Format: Article
• Language: English
• Published: 2013-03-01.
• Subjects: Article
• Online Access: Get fulltext; Get fulltext

 Complex systems, which consist of different interdependent and interlocking subsystems, typically have multiple equilibrium points associated with different set points of each operation mode. These systems are usually interpreted as switched systems, or in general, as hybrid systems. Surprisingly, the consideration of multiple equilibria is not common in hybrid systems' literature, being typically focused on the study of stability and dissipativity properties for switched systems whose subsystems share the same equilibrium point. This paper will expand the discussion to the case of having multiple co-existing equilibrium points for hybrid systems modelled as hybrid automata, which are more general than switched systems. A classification of equilibria for hybrid automata is offered, and some stability related properties are shown for them. Moreover, some dissipativity-related properties are studied. The chief idea of our approach is to identify stable and dissipative components as group of discrete locations within the hybrid automaton. Two examples are used to illustrate our conclusions.