Robust induced ℓ2-ℓ∞ optimal control of discrete-time systems having magnitude and rate-bounded actuators

Ibrahim Kucukdemiral, Xiaoran Han, Mustafa Suphi Erden

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The design of robust state- and output-feedback control for uncertain discrete-time systems with physical magnitude and rate constraints on their actuator dynamics was addressed. Unlike the traditional methods such as anti-windup (AW) methods, nested ellipsoids, model predictive controllers (MPCs) and integral quadratic constraints(IQCs) formulated by sector bounded inequalities, this paper uses a transformation of the system dynamics to a form which considers control signal and its rate as controlled outputs and using discrete-time ℓ induced (peak-to-peak) norm from disturbance inputs to these outputs. To cope with the magnitude and rate bound non-linearities together, the induced ℓ norm from disturbance input to the outputs involving control signal and its rate is utilised. On the other hand, discrete-time(DT) induced ℓ 2 norm from disturbance input to the main controlled output is used to mitigate the effects of disturbances. We can tackle this ambitious non-linear control problem in the domain of linear convex multi-objective optimal control problem, which can be solved by effective semi-definite optimisation methods by using the proposed transformation and handling the control constraints in terms of worst case peak-to-peak gain of the system. Extended Linear Matrix Inequalities (LMIs) and full block S-procedure based design conditions developed over Linear Fractional Representation(LFR) framework allow the user to obtain robust state- and output-feedback control solutions with reduced conservatism. For the first time, this paper introduces an extended LMI based robust output-feedback control design for magnitude and rate bounded (MRB) systems, using full block S-procedure. We demonstrate the performance of the proposed controller through several simulations over benchmark examples covering systems having multi-variable structures and uncertainties. Our study also involves comparison results with a recently introduced technique based on multi-stage AW technique. The simulation results show that the proposed method of this paper is much effective and less conservative compared to the recent AW method provided in the literature.

Original languageEnglish
Pages (from-to)73-87
Number of pages15
JournalISA Transactions
Issue numberPart B
Early online date22 Feb 2022
Publication statusPublished - Oct 2022


  • Discrete-time systems
  • LMIs
  • Magnitude and rate-bounded systems
  • Robust control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Instrumentation
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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