Robust State-Feedback Controllability of Linear Systems to a Hyperplane in a Class of Bounded Controls

V. Turetsky and V. Y. Glizer
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V. Turetsky: Technion-Israel Institute of Technology
V. Y. Glizer: Technion-Israel Institute of Technology

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 3, No 10, 639-667

Abstract: Abstract The paper deals with a linear time-dependent dynamic system with scalar control and input uncertainty (disturbance). Two admissible classes of input uncertainty realizations are considered: the class of measurable bounded functions and the class of measurable quadratically integrable functions. The problem to be studied is the existence of a state feedback control with measurable bounded time realizations transferring the system to a given hyperplane (a target set) from any initial position in a prescribed time for any admissible input uncertainty realization. Necessary and sufficient conditions for the existence of such a control are derived, based on the explicit construction of this control by using an auxilary zero-sum linear-quadratic differential game with a cheap control for the minimizing player. Examples illustrting the theoritical results are presented.

Keywords: Dynamic systems; input uncertainties; robust controllability; state-feedback control; differential games; cheap control (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s10957-004-5727-y

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