| Kalman's Controllability Rank Condition: From Linear To Nonlinear (2007) | |||||||||||||||
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| The notion of controllability was identified by Kalman as one of the central properties determining system behavior. His simple rank condition is ubiquitous in linear systems analysis. This article presents an elementary and expository overview of the generalizations of this test to a condition for testing accessibility of discrete and continuous time nonlinear systems. 1 Introduction The state-space approach to control systems analysis took center stage in the late 50's. Right from the beginning, it was recognized that certain nondegeneracy assumptions were needed in establishing results on optimal control. However, it was not until Kalman's work ([9], [10]) that the property of controllability was isolated as of interest in and of itself, as it characterizes the degrees of freedom available when attempting to control a system. The study of controllability for linear systems, first carried out in detail by Kalman and his coworkers in [10], has spanned a great number of research dire... | |||||||||||||||
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