Theory of residence-time control by output feedback (Q1179526)

This paper deals with an Itô stochastic control system \(dx=(Ax+Bu)dt+\varepsilon C dw\), \(y=Dx\), where \(x\in\mathbb{R}^ n\), \(u\in\mathbb{R}^ m\), \(y\in\mathbb{R}^ p\), \(w(t)\) is an \(r\)-dimensional standard Brownian motion, \(\varepsilon>0\) is a small parameter and \(A\), \(B\), \(C\), \(D\) are suitable constant matrices. The solutions of this system are considered within a given bounded domain \(\Omega\) of \(y\)-space \(\mathbb{R}^ p\). The specific problem addressed is the control of the residence-time in \(\Omega\), implemented by an observer-based output feedback with either exact or noise-corrupted observations. It is shown that in the case of exact observations, bounds can be given of the achievable residence-time in terms of the phase-zeros of the system. When the measurement is noisy, the achievable residence-time is shown to be always bounded and a corresponding estimate is given. Related criteria for system design are given and an example is presented.