The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

Abstract

In this paper we deal with the mixed  ∞ /finite-time stability control problem. More specifically, given an open loop uncertain linear system, we provide a necessary and sufficient condition for quadratic input-output finite-time stability with an  ∞ bound. Exploiting this result we also give a sufficient condition to solve the related synthesis problem via state-feedback. The property of quadratic input-output finite-time stability with an  ∞ bound implies that the system under consideration satisfies an  ∞ performance bound between the disturbance input and the controlled output and, at the same time, is input-output finite-time stable for all admissible uncertainties. This condition requires the solution of a feasibility problem constrained by a pair of differential linear matrix inequalities (LMIs) coupled with a time-varying LMI. The proposed technique is illustrated by means of both a numerical and a physical example.

On finite time stability with guaranteed cost control of uncertain linear systems

“…A similar multi-objective problem has been considered in [7], but in the context of Input Output Finite Time Stability (IO-FTS). In this case initial conditions of the controlled system are zero, but the system is subject to a disturbance input; IO-FTS and a H ∞ bound are then simultaneously considered.…”

“…Here we consider the different case where the initial conditions are not zero, and instead of an H ∞ constraint we consider a quadratic integral cost constraint. Moreover differently from [7], our approach allows to explicitly consider actuator constraints. Note that, although not directly discussed in the paper, the presence of external disturbances can be taken into account in our design methodology, if these disturbances can be generated by an autonomous exo-system (it will be sufficient to apply our design methodology to a suitable augmented system).…”

Finite-Time Boundedness and H∞ Control for Affine Switched Systems

“…The authors [21,22] applied FTS/FTB conceptions to switched systems and compared the conservativeness among different conditions. In [23], the mixed ∞ /finite-time stability control problem was discussed. For quadratic input-output finite-time stability with an ∞ bound, [23] provided a 2 Mathematical Problems in Engineering necessary and sufficient condition.…”

“…In [23], the mixed ∞ /finite-time stability control problem was discussed. For quadratic input-output finite-time stability with an ∞ bound, [23] provided a 2 Mathematical Problems in Engineering necessary and sufficient condition. Then the method was extended to robust ∞ controller and filter design for switched system with exogenous noise [24,25].…”