Stabilisation of multiply-time-delayed sampled-data systems via quasi ℋ∞ control designed with DLMI

Abstract

This paper considers stabilisation of a class of multiply-time-delayed (MTD) sampled-data systems via variation-of-constant discretisation (VOCD) re-modelling and discrete-time performance control optimisation. More precisely, by utilising the variation-of-constants formula for solutions to functional differential equations, discrete-time re-modelling of sampled-data systems with MTD plants is derived, which yields finite-dimensional linear time-invariant discrete models with augmented states. Based on the VOCD re-modelling, structural features and dynamics of the MTD sampled-data systems are examined in the discrete-time approximation sense, and then stabilisation is achieved by means of the performance controller design with the discrete linear matrix inequalities (DLMI). This provides us with necessary and sufficient conditions in stabilisation and the controller parametrisation is numerically tractable in the DLMI sense. Numerical examples are included to illustrate effectiveness of the proposed method.