Stability of linear autonomous systems under regular switching sequences

Switched systems;Muller Automata;Robust stability

Wang, Yu ; Dullerud ; Geir E.

关键词: Switched systems;    Muller Automata;    Robust stability;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/50614/Yu_Wang.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this work, we discuss the stability of a discrete-time linear autonomous systemunder regular switching sequences, whose switching sequences are generated bya Muller automaton. This system arises in various engineering problems such asdistributed communication and automotive engine control. The asymptotic stabilityof this system, referred to as regular asymptotic stability, generalizes twowell-known definitions of stability of autonomous discrete-time linear switchedsystems, namely absolute asymptotic stability (AAS) and shuffle asymptotic stability(SAS). We also extend these stability definitions to robust versions. Weprove that absolute asymptotic stability, robust absolute asymptotic stability androbust shuffle asymptotic stability are equivalent to exponential stability. In addition,by using the Kronecker product, we prove that a robust regular asymptoticstability problem is equivalent to the conjunction of several robust absoluteasymptotic stability problems.