Linear Discrete-time Dissipative Systems

Dissipativity is an important unifying concept across systems and control theory, being a generalisation of the concept of energy and the stability methods of Lyapunov. This thesis concerns discrete-time dissipative systems, and its main goal is to present versions of the discrete-time positive real and discrete-time bounded real lemmas that do not require the assumptions of controllability and observability, and in fact require no assumptions at all. The optimal control problem associated with passive systems is solved, likewise for non-expansive systems. A brief history of dissipativity is discussed, with particular highlighting of the context of the Cold War and the choice of names for concepts in Systems and Control theory.<p></p>

Author dc:creator

• Edward Branford (21038150)

• Linear systems
• dissipative systems
• passive systems
• discrete-time positive real lemma
• discrete-time bounded real lemma
• optimal control
• time-invariant systems

Statement dc:rights

• All rights reserved
• Open Access after 2027-07-12

Identifier

10779/exe.31231519.v1

OAI identifier oai:identifier

oai:figshare.com:article/31231519