Simultaneous Design of Linear Time-Invariant Systems using Generalized Sampled-Data Hold Functions

Abstract

This paper studies the use of generalized sampled-data hold functions (GSHF) in the problem of simultaneous design of linear time-invariant control systems. The simultaneous design problem can be stated as follows. Given plants P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , ..., P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</inf> , find one single controller C that achieves simultaneous stability, or simultaneous optimal quadratic performance in the N given systems. The idea of GSHF is to periodically sample the output of a system, and generate the feedback control law by means of periodically time-varying hold functions which are applied to the sample sequence. GSHF control considers the hold functions as design parameters which are chosen based on the dynamics of the systems to be controlled. Applying GSHF to the simultaneous design problem, we give solutions in three aspects: simultaneous stabilization, simultaneous optimal quadratic performance, and simultaneous pole assignment in combination with simultaneous inter-sampling performance.