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This note focuses on the static output feedback stabilization problem for a class of single-input-single-output systems when the control law includes multiple (distinct) delays. We are interested in giving necessary conditions for the existence of such stabilizing controllers. Illustrative examples (second-order system, chain of integrators, or chain of oscillators) are presented, and discussed. Index Terms--Asymptotic stability, delay, quasi-polynomial.

Quasi-polynomial families generated by multivariate interval polynomials are considered. It is shown that for these families both delay independent and delay dependent vertex-type stability conditions hold. Index Terms--Multivariate polynomials, robust stability, time-delay systems, vertex-type stability conditions.

Summary: The robust stability of linear systems with both state and input delay in closed loop with dynamic predictor‐based controller is analyzed. The problem of time‐varying matrix uncertainty is studied in the Lyapunov‐Krasovskii framework. The complete type functional with prescribed derivative expressed in terms of the delay Lyapunov matrix associated with the nominal system is a key piece of our analysis. The robust stability conditions depend on the delay Lyapunov matrix whose computation is carried out. An illustrative example is presented. [ABSTRACT FROM AUTHOR]

In this paper, some recent results on additional dynamics for transformed time-delay systems are extended to the case of time-varying systems. Special equations which describe these dynamics are derived. Additional restrictions on stability and robust stability imposed by the transformations are obtained. [Copyright &y& Elsevier]