Research On Passive Control And Exponentially Passive Control For Uncertain Discrete-time Systems

Passivity as a special case of the dissipation widely exists in applied mathematics, physics, astronautics and other fields. This paper mainly researches on passive control and exponentially passive control problems for uncertain discrete-time systems, the full text main content is as follows:(1) Firstly, we introduce the development of the theory of dissipative control, current research status, the research background and significance; Secondly, we introduce passivity as a special case of the concept of dissipation; Finally, we illustrate the arrangement of the content and structure of the research.(2) We research on the passive control of uncertain discrete systems with time-varying parameters. Firstly, we give sufficient and necessary conditions when the uncertain discrete systems with time-varying parameters are passive, then we design the passive controller and give the numerical example to verify the feasibility of the theorem; Secondly, we get the definition of discrete exponential passivity by the definition of exponential passivity; Finally, we give sufficient and necessary conditions when the uncertain discrete systems with time-varying parameters are exponentially passive, then we design the passive controller and give the numerical example to verify the feasibility of the theorem.(3) We research on the passive control of uncertain discrete systems with time-varying delay. We give the sufficient condition when the uncertain discrete systems with time-varying delay are exponentially passive, then we design the passive controller and give the numerical example to verify the feasibility of the theorem.(4) We research on the passive control of generalized uncertain discrete systems with time-varying delay. We give the sufficient condition when the uncertain discrete systems with time-varying delay are exponentially passive, then design the passive controller and give the numerical example to verify the feasibility of the theorem.(5) We summarize this paper.