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

Purpose - This 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/approach - The 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. Findings - A 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/implications - The proposed approach can be used in the analysis and design of the uncertain multivariable time-delay systems. Originality/value - The 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.