Pre-classical tools for post-modern control

In this paper, we present a systematic optimal and robust control theory (for SISO systems) in a language suitable for undergraduate teaching. The tools used are mostly simple polynomial arithmetics and elementary linear algebra. The theory covers almost all topics that post-modern control concerns: the computation of the RMS value (2-norm) of a signal or a system, the computation of the resonance peak (∞-norm) of a system, and the computation of the Hankel singular values and vectors, optimal transient stabilization (LQG control), optimal robust stabilization with respect to the Vinnicombe metric (H_∞ control), and system approximation. A systematic synthesis theory is presented based on the pole placement technique, which is equivalent to solving a polynomial diophantine equation.