Measurement stability of time-optimal feedback control of two-input strictly normal linear systems (Q914598)

Given a linear, time-independent system of the form \(\dot x(t)=Ax(t)+Bu(t)\), where the input space is two dimensional and \(| u_ i(t)| \leq 1\), \(i=1,2\). The paper is concerned with the time- optimal control of such a system. Under the assumption that the optimal control is given by a (nonlinear) feedback law the author studies the stability with respect to measurement of the closed-loop system. This form of stability is by definition that the solutions of \(\dot x(t)=f(x(t))\) and \(\dot x(t)=f(x(t)+p(t))\) are close for p small. The main result of this paper is a complete characterization of all systems for which the closed-loop, time-optimal control system is stable with respect to measurement. The test is given in the coefficients A and B.