Finite-Time Output Feedback Control of Linear Systems via Differential Linear Matrix Conditions

Abstract

This paper deals with the finite-time output feedback control problem for continuous-time, time-varying linear systems. Sufficient conditions for the existence of a controller which finite-time stabilizes the closed loop system are provided, both for the state feedback and the output feedback case. Such conditions are given in terms of a feasibility problem involving Riccati differential equations and differential linear matrix inequalities.

Soft Controller Switching with Guaranteed H∞ Performance

“…The conditions of Lemma 1, as well as the conditions derived below are DLMIs which can be solved using the method of [Amato et al (2006)] as explained above.…”

“…In order to obtain LMI conditions we apply the method of [Amato et al (2006)] to Theorem 1, without dividing the interval t ∈ [0, T ] into smaller subsections. This naturally leads to a conservative design.…”

“…We use the above theorems, as well as the corollaries for the design. When we use the theorems, we divide the SSI into sections of equal length and use the method of [Amato et al (2006)] to obtain LMIs.…”

“…DLMIs are infinite dimensional conditions, and an optimal solution requires one to find a non-countable number of parameters, which is computationally infeasible. A computationally efficient method for solving DLMIs has been presented in [Amato et al (2006)], where the DLMIs are converted into LMIs. In [Amato et al (2006)] is is assumed that the decision variables are all piecewise-linear in time, with a predetermined number of sections.…”

“…A computationally efficient method for solving DLMIs has been presented in [Amato et al (2006)], where the DLMIs are converted into LMIs. In [Amato et al (2006)] is is assumed that the decision variables are all piecewise-linear in time, with a predetermined number of sections. The value of the decision variables is then found at the vertices of these sections.…”