Kalman’s Contributions to Control Theory

Rudolf Emil Kalman was a Hungarian-American electrical engineer and mathematician who revolutionized the field of control theory by introducing advanced mathematical techniques for studying control systems. In particular, he popularized the “Time-Domain Approach” for studying Linear Time-Invariant (LTI) systems over the traditional “Frequency-Domain Approach” that was typically used before his work. To contrast these approaches briefly, in the former approach, one works with the LTI system directly in the time-domain, whereas in the latter approach, one works with the transfer function, which relates the input of the LTI system to its output in the frequency domain. This was, in fact, one of his major contributions to control theory, since he showed that many fundamental properties of LTI systems can be deduced directly by taking his alternative approach, which otherwise would have been difficult (or maybe even impossible) to establish using the traditional approach. This expository article is an attempt to highlight only a few of his ingenious contributions to control theory.