Stability of linear autonomous systems under regular switching sequences

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

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Wang, Yu

Contributors dc:contributor

• Dullerud, Geir E.

• Switched systems
• Muller Automata
• Robust stability

Statement dc:rights

• Copyright 2014 Yu Wang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/50614

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/50614