Delay-dependent Robust Stabilization for Systems with Time-varying Delays

Delay-dependent Robust Stabilization for Systems with Time-varying Delays

This paper extends the results of the stability criterion, introduced in the literature, to the problem of stabilization for systems with time-varying delays. Unfortunately, the delay-dependent stabilization conditions using state/output-feedback controllers are not formulated as LMIs. To achieve a better degree of freedom in relaxing the resultant nonlinear terms, we do not assume any restriction on the form of variables, which is a generally adopted procedure in the structure-imposing relaxation methods. Instead, we develop a congruence transformation that has the effect of gathering the dispersed nonlinear terms and bundling them together into fewer and more intensive non-convex conditions. To relax these, an efficient iterative algorithm is proposed in the form of two-phase-based convex optimization problem. Numerical examples show that the results obtained by these criteria improve the allowable maximal delays over the existing results in the literature.

This paper extends the results of the stability criterion, introduced in the literature, to the problem of stabilization for systems with time-varying delays. Unfortunately, the delay-dependent stabilization conditions using state/output-feedback controllers are not formulated as LMIs. To achieve a better degree of freedom in relaxing the resultant nonlinear terms, we do not assume any restriction on the form of variables, which is a generally adopted procedure in the structure-imposing relaxation methods. Instead, we develop a congruence transformation that has the effect of gathering the dispersed nonlinear terms and bundling them together into fewer and more intensive non-convex conditions. To relax these, an efficient iterative algorithm is proposed in the form of two-phase-based convex optimization problem. Numerical examples show that the results obtained by these criteria improve the allowable maximal delays over the existing results in the literature.