A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

Abstract

This paper addresses the non-fragile control problem for a class of uncertain linear systems subject to model uncertainty, controller perturbations, fault signals and input constraints. The controller to be designed is supposed to have additive gain perturbations. A novel state feedback controller is proposed based on the exact available expectation of a Bernoulli random variable, which is introduced to model the feature of the controller gain perturbation that randomly occurs. By using Lyapunov stability theory, new sufficient conditions are derived to design non-fragile controller for a class of uncertain linear systems considering input constraints. Compared with the existing non-fragile state feedback controller methods, the non-fragile property is fully considered to improve the tolerance of uncertainties in the controller, where the conservativeness can be reduced via the Bernoulli random variable. The effectiveness of the proposed control strategy is illustrated by two numerical examples.

A RobustH∞ Fault Tolerant Controller for Uncertain Systems Described by Linear Fractional Transformation Model

“…The uncertain term ∆∈ ℝ × would be extracted by a suitable selection of some internal signals ( ) ∈ ℝ and ( ) ∈ ℝ . Compared to the existing studies [8,48,49], the differential equation ( 5) would be a more general form to represent the uncertainty. Thus many uncertain systems (for instants [8,48]) can be described via Eq.…”

“…Compared to the existing studies [8,48,49], the differential equation ( 5) would be a more general form to represent the uncertainty. Thus many uncertain systems (for instants [8,48]) can be described via Eq. (5).…”

“…The previous work [48] is a special case of the uncertain system (5) with 22 = 0, ℬ 2 = 0 , 2 = 0, and 2 ( ) = 0. Thus, it is considered as follows:…”

“…Additionally, it is guaranteed that the infinite gain of the uncertain system (7) would be less than or equal to . Consequently, ignoring the nonlinear function, the results are reduced to the existing method [48].…”

“…Then robust ∞ output regulation of an uncertain LFT system is investigated in [47]. Lately, employing the additive uncertainties, an LMI method is addressed to the ∞ control design [48]. But such a method would not be effective in the presence of other types of uncertainties.…”