Title: D-stability of parameter-dependent linear systems including discretisation by Taylor series expansion and search in a scalar parameter

Authors: Marco Aurélio Carvalho Leandro; Karl Heinz Kienitz

Addresses: Department of Systems and Control, Aeronautics Institute of Technology, IEE-ITA-DCTA, São José dos Campos, SP, 12228-900, Brazil ' Department of Systems and Control, Aeronautics Institute of Technology, IEE-ITA-DCTA, São José dos Campos, SP, 12228-900, Brazil

Abstract: This work addresses the allocation of closed-loop poles of a discretised system from a continuous-time one with varying parameters, aiming at its control through a computer. It proposes a sufficient condition for an allocating state feedback with parameter-dependent gain. The condition is verified through a feasibility test of a set of linear matrix inequalities (LMIs), based on the existence of a homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree. The main contribution of this work is the guarantee of the continuous-time system's stability and simultaneously the allocation of the closed-loop poles of the discretised system in a D-stable region. In order to allow this, the discretised model is formed by homogeneous polynomial matrices of arbitrary degree, augmented by an additive norm-bounded term, which represents the discretisation residual error. Numerical examples show a larger number of feasible cases associated with the proposed condition in comparison with the condition based on a parameter-independent gain.

Keywords: Robust control; D-stability; discrete-time linear systems; parameter-dependent state feedback; linear matrix inequalities.

DOI: 10.1504/IJMIC.2019.099811

International Journal of Modelling, Identification and Control, 2019 Vol.31 No.4, pp.303 - 313

Received: 29 Sep 2016
Accepted: 15 May 2017
Published online: 23 May 2019 *

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