Switched Markov Jump Linear Systems: Analysis and Control Synthesis

Markov 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Electrical Engineering

Department dc:contributor.department

Electrical and Computer Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2014

Author dc:creator

• Lutz, Collin C.

Chair dc:contributor.committeechair

• Stilwell, Daniel J.

Committee members dc:contributor.committeemember

• Ravindran, Binoy
• Woolsey, Craig A.
• Beex, Aloysius A.
• Baumann, William T.

• Time-inhomogeneous Markov jump linear systems
• switched Markov jump linear systems
• stochastic systems
• stochastic optimal control
• networked control
• control over communications
• fault-tolerant control
• energy-aware control

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:3903

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/50859