Finite time H<inf>&#x221E;</inf> controller design based on finite time H<inf>&#x221E;</inf> functional filter for linear continuous systems

Abstract

In this paper we investigate the problem of the design of a controller based on H∞ functional filter, in a finite time stability context for linear continuous time-invariant systems affected by norm bounded disturbances. The finitetime H∞ boundedness criterion of the closed-loop system is investigated. The order of the controller is reduced since the designed functional filter has the same order than the dimension of the control input of the system. The design conditions are expressed as linear matrix inequalities. A numerical example is provided to show the validity of the proposed approach.978-1-4799-8318-6/15/$31.00 ©2015 IEEE

Results on finite‐time boundedness and finite‐time control of non‐linear quadratic systems subject to norm‐bounded disturbances

“…which contradicts equality (14). Then, an instant t 1 < T f does not exist, therefore any trajectory x(0) that starts from 0 does not come out of ℰ 1 , ∀t ∈ [0, T f ], ∀w( ⋅ ) ∈ d 2 .…”

“…There have been several developments in the field of FTS and FTB for linear systems (see e.g. [12][13][14][15] and references therein). However, to our knowledge, the study of FTS and FTB of nonlinear systems is still in its infancy.…”