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On the Stabilization of a Network of a Class of SISO Coupled Hybrid Linear Subsystems via Static Linear Output Feedback

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  • Manuel De la Sen

    (Department of Electricity and Electronics, Faculty of Science and Technology, Institute of Research and Development of Processes, University of the Basque Country (UPV/EHU), 48940 Leioa, Bizkaia, Spain)

Abstract

This paper deals with the closed-loop stabilization of a network which consists of a set of coupled hybrid single-input single-output (SISO) subsystems. Each hybrid subsystem involves a continuous-time subsystem together with a digital (or, eventually, discrete-time) one being subject to eventual mutual couplings of dynamics and also to discrete delayed dynamics. The stabilizing controller is static and based on linear output feedback. The controller synthesis method is of algebraic type and based on the use of a linear algebraic system, whose unknown is a vector equivalent form of the controller gain matrix, which is obtained from a previous algebraic problem version which is based on the ad hoc use of the matrix Kronecker product of matrices. As a first step of the stabilization, an extended discrete-time system is built by discretizing the continuous parts of the hybrid system and to unify them together with its digital/discrete-time ones. The stabilization study via static linear output feedback contains several parts as follows: (a) stabilizing controller existence and controller synthesis for a predefined targeted closed-loop dynamics, (b) stabilizing controller existence and its synthesis under necessary and sufficient conditions based on the statement of an ad hoc algebraic matrix equation for this problem, (c) achievement of the stabilization objective under either partial or total decentralized control so that the whole controller has only a partial or null information about couplings between the various subsystems and (d) achievement of the objective under small coupling dynamics between subsystems.

Suggested Citation

  • Manuel De la Sen, 2022. "On the Stabilization of a Network of a Class of SISO Coupled Hybrid Linear Subsystems via Static Linear Output Feedback," Mathematics, MDPI, vol. 10(7), pages 1-29, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1066-:d:779855
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    References listed on IDEAS

    as
    1. Li Wang, 2020. "Numerical Algorithms of the Discrete Coupled Algebraic Riccati Equation Arising in Optimal Control Systems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, August.
    2. M. de la Sen, 2005. "Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics," Discrete Dynamics in Nature and Society, Hindawi, vol. 2005, pages 1-31, January.
    3. Li Wang, 2020. "An Improved Iterative Method for Solving the Discrete Algebraic Riccati Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-6, May.
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