Switched Markov Jump Linear Systems: Analysis and Control Synthesis

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dc.contributor.authorLutz, Collin C.en
dc.contributor.committeechairStilwell, Daniel J.en
dc.contributor.committeememberRavindran, Binoyen
dc.contributor.committeememberWoolsey, Craig A.en
dc.contributor.committeememberBeex, Aloysius A.en
dc.contributor.committeememberBaumann, William T.en
dc.contributor.departmentElectrical and Computer Engineeringen
dc.date.accessioned2014-11-15T09:00:09Zen
dc.date.available2014-11-15T09:00:09Zen
dc.date.issued2014-11-14en
dc.description.abstractMarkov jump linear systems find application in many areas including economics, fault-tolerant control, and networked control. Despite significant attention paid to Markov jump linear systems in the literature, few authors have investigated Markov jump linear systems with time-inhomogeneous Markov chains (Markov chains with time-varying transition probabilities), and even fewer authors have considered time-inhomogeneous Markov chains with a priori unknown transition probabilities. This dissertation provides a formal stability and disturbance attenuation analysis for a Markov jump linear system where the underlying Markov chain is characterized by an a priori unknown sequence of transition probability matrices that assumes one of finitely-many values at each time instant. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities (LMIs) that can be solved efficiently. These finite-dimensional LMI analysis results lead to nonconservative LMI formulations for optimal controller synthesis with respect to disturbance attenuation. As a special case, the analysis also applies to a Markov jump linear system with known transition probabilities that vary in a finite set.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:3903en
dc.identifier.urihttp://hdl.handle.net/10919/50859en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectTime-inhomogeneous Markov jump linear systemsen
dc.subjectswitched Markov jump linear systemsen
dc.subjectstochastic systemsen
dc.subjectstochastic optimal controlen
dc.subjectnetworked controlen
dc.subjectcontrol over communicationsen
dc.subjectfault-tolerant controlen
dc.subjectenergy-aware controlen
dc.titleSwitched Markov Jump Linear Systems: Analysis and Control Synthesisen
dc.typeDissertationen
thesis.degree.disciplineElectrical Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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