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A method for the reduction of interactions in linear time invariant (LTI) multivariable uncertain systems is proposed. An H∞-norm metric is proposed for the assessment of interactions in interval uncertain multiple-input multiple-output (MIMO) plants. Based on this, a procedure for the design of fixed-order dynamic decoupling precompensators for MIMO plants with interval uncertainty is outlined which can be solved using efficient solvers such as CVX. The proposed methodology is used to develop a low-order robust multivariable controller for voltage and frequency control of an islanded distributed generation (DG) unit. Copyright © 2017 by ASME  

This article deals with stabilization of Lotka-Volterra (LV) systems in the presence of interval uncertainty and a physical limitation on the control input, which restricts this input to be strictly positive. Considering the positiveness property of LV systems, a quasi-monomial structure for the state feedback based control input is proposed. Considering this structure, stability of the closed-loop system with no uncertainty is analyzed. This analysis leads to an algebraic inequality, whose satisfaction guarantees stability of the closed-loop system. To extend this result to uncertain LV systems with interval parameter uncertainty, a new approach, by which stability of the positive... 

We propose a robust deviation framework to deal with uncertain component reliabilities in the constrained redundancy optimization problem (CROP) in series-parallel reliability systems. The proposed model is based on a linearized binary version of standard nonlinear integer programming formulations of this problem. We extend the linearized model to address uncertainty by assuming that the component reliabilities belong to an interval uncertainty set, where only upper and lower bounds are known for each component reliability, and develop a Min-Max regret model to handle data uncertainty. A key challenge is that, because the deterministic model involves nonlinear functions of the uncertain... 

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order α is a known constant belonging to 0 < α < 1. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and... 

This paper proposes a novel representation of uncertain LTI fractional order systems based on the state-space model which contains both interval and polytopic uncertainties. First, a set of linear matrix inequalities, which are sufficient conditions, are presented for analyzing the robust stability of the mentioned systems. Then, some sufficient conditions are obtained for designing a feedback gain matrix to tackle the robust stabilization of the considered systems. Note that the concluded conditions of this paper are valid for fractional systems with a given constant derivative order α in 1 ≤ α < 2 and also, can be employed conservatively for α in 0 < α < 1. Finally, through two numerical... 

This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka-Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all...