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A study of strong stability of distributed systems. ph.d. thesis
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Cataltepe, Tayfun |
| Copyright Year | 1989 |
| Description | The strong stability of distributed systems is studied and the problem of characterizing strongly stable semigroups of operators associated with distributed systems is addressed. Main emphasis is on contractive systems. Three different approaches to characterization of strongly stable contractive semigroups are developed. The first one is an operator theoretical approach. Using the theory of dilations, it is shown that every strongly stable contractive semigroup is related to the left shift semigroup on an L(exp 2) space. Then, a decomposition for the state space which identifies strongly stable and unstable states is introduced. Based on this decomposition, conditions for a contractive semigroup to be strongly stable are obtained. Finally, extensions of Lyapunov's equation for distributed parameter systems are investigated. Sufficient conditions for weak and strong stabilities of uniformly bounded semigroups are obtained by relaxing the equivalent norm condition on the right hand side of the Lyanupov equation. These characterizations are then applied to the problem of feedback stabilization. First, it is shown via the state space decomposition that under certain conditions a contractive system (A,B) can be strongly stabilized by the feedback -B(*). Then, application of the extensions of the Lyapunov equation results in sufficient conditions for weak, strong, and exponential stabilizations of contractive systems by the feedback -B(*). Finally, it is shown that for a contractive system, the first derivative of x with respect to time = Ax + Bu (where B is any linear bounded operator), there is a related linear quadratic regulator problem and a corresponding steady state Riccati equation which always has a bounded nonnegative solution. |
| File Size | 2806009 |
| Page Count | 102 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19910005453 |
| Archival Resource Key | ark:/13960/t9c58hf0g |
| Language | English |
| Publisher Date | 1989-12-01 |
| Access Restriction | Open |
| Subject Keyword | Linear Systems Liapunov Functions Systems Stability Operators Mathematics Control Stability Hilbert Space Decomposition Control Theory Feedback Control Riccati Equation Distributed Parameter Systems Linear Quadratic Regulator Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Thesis |
