Stability criteria for feedback-controlled, imperfectly known, bilinear systems with time-varying delay

The problem of synthesizing a class of continuous, memoryless feedback controls in order to stabilize a class of imperfectly known homogeneous-in-the-state bilinear time-delay systems is considered. In particular, bilinear systems with state time-delay in the linear term are investigated. The time-d...

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Bibliographic Details
Published in:Mathematics and computers in simulation 1998-02, Vol.45 (3), p.279-289
Main Author: Goodall, David P.
Format: Article
Language:English
Subjects:
Applied sciences
Calculus of variations and optimal control
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Mathematical analysis
Mathematics
Sciences and techniques of general use
System theory
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Summary:The problem of synthesizing a class of continuous, memoryless feedback controls in order to stabilize a class of imperfectly known homogeneous-in-the-state bilinear time-delay systems is considered. In particular, bilinear systems with state time-delay in the linear term are investigated. The time-delay is assumed to be an unknown time-varying function with known upper bound on its derivative. As well as considering both matched and residual uncertainty, the uncertainty in the class of systems can be state, delayed-state and input dependent, and time-varying. Prior information on the bound of the system uncertainty is required; such bounding information allows for quadratic growth with respect to the state. For this stabilizability problem, a stability criterion, involving the upper bound on the derivative of the time-varying time-delay is obtained.
ISSN:0378-4754
1872-7166
DOI:10.1016/S0378-4754(97)00107-9