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.