Robust stabilization of input‐delayed systems with design example for rocket motor control

Abstract

PurposeThis paper aims to use a new design approach based on a Lagrange mean value theorem for the stabilization of multivariable input‐delayed system by linear controller.Design/methodology/approachThe delay‐dependent asymptotical stability conditions are derived by using augmented Lyapunov‐Krasovskii functionals and formulated in terms of conventional Lyapunov matrix equations and some simple matrix inequalities. Proposed design approach is extended to robust stabilization of multi‐variable input‐delayed systems with unmatched parameter uncertainties. The maximum upper bound of delay size is computed by using a simple optimization algorithm.FindingsA liquid monopropellant rocket motor with a pressure feeding system is considered as a numerical design example. Design example shows the effectiveness of the proposed design approach.Research limitations/implicationsThe proposed approach can be used in the analysis and design of the uncertain multivariable time‐delay systems.Originality/valueThe paper has a great potential in the stability analysis of time‐delay systems and design of time‐delay controllers and may openup a new direction in this area.