Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


ohiou1187704023.pdf (715.66 KB)

ETD Abstract Container

Abstract Header

Linear Impulsive Control Systems: A Geometric Approach

Medina, Enrique A.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1187704023

Abstract Details

2007, Doctor of Philosophy (PhD), Ohio University, Electrical Engineering & Computer Science (Engineering and Technology).
Linear impulsive systems are a class of hybrid systems in which the state propagates according to linear continuous-time dynamics except for a countable set of times at which the state can change instantaneously. These systems are useful in representing a number of real world applications, including the problem of drug distribution in the human body, management of renewable resources, spacecraft guidance and control, and sampled-data control systems with consideration of inter-sample behavior. While in general the impulsive effects can be time-driven and/or event-driven, this work focuses on the time-driven case. This study of linear impulsive systems starts by addressing the fundamental concepts of reachability and observability, and shows that these properties depend on whether the impulse times are fixed or free. A geometric characterization of reachable and unobservable sets in terms of invariant subspaces is developed, and algorithms for their construction are established. In particular, the concept of strong reachability, introduced here, enables the formulation of a state-feedback stabilization method for linear impulsive systems that possess these properties. When the open-loop system is strongly reachable, the weighted reachability gramian can be guaranteed to be uniformly positive definite as long as each time interval under consideration contains a sufficient number of impulses, and its inverse can be used to formulate a state feedback law that stabilizes the impulsive system even when the impulse times are not uniformly spaced. An output stabilization problem is formulated and translated into geometric terms starting with the concepts of controlled-invariant and conditioned-invariant subspaces for linear impulsive systems, for which we provide definitions and algorithms for computation. By relating controlled-invariant and conditioned-invariant subspaces of the open-loop impulsive system to invariant subspaces of the corresponding closed-loop system, it becomes possible to establish sufficient conditions for solution of the output stabilization problem. The examples illustrate the reachability and observability characterization, exercise the state-feedback control law design method, and demonstrate the compensator synthesis method on a reference tracking control system design problem. Finally some conclusions and recommendations for further work are presented.
Douglas Lawrence (Advisor)
122 p.
Linear Impulsive Control Systems; Impulsive Systems; Controlled and Conditioned Invariant Subspaces; Geometric Control; Linear System Theory; Control Systems

Recommended Citations

Citations

  • Medina, E. A. (2007). Linear Impulsive Control Systems: A Geometric Approach [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1187704023

    APA Style (7th edition)

  • Medina, Enrique. Linear Impulsive Control Systems: A Geometric Approach. 2007. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1187704023.

    MLA Style (8th edition)

  • Medina, Enrique. "Linear Impulsive Control Systems: A Geometric Approach." Doctoral dissertation, Ohio University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1187704023

    Chicago Manual of Style (17th edition)

ohiou1187704023
2,719
© 2007, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.