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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.

This note focuses on the stability of some class of delay systems, including uncertainty in the delays. More precisely, we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system. If the delay perturbation is constant, necessary and sufficient conditions are derived in terms of generalized eigen-value distribution of some (finite-dimensional) constant matrix pencil. If the delay perturbation is time-varying, some sufficient stability conditions are derived using "exact" Lyapunov--Krasovskii functionals. Illustrative examples are also included. Index Terms--Delay, Lyapunov functionals, matrix pencils, uncertainty.

There are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coefficient space: The Edge Theorem and the theory based on the concept of convex directions. Many known results can be explained with these two results. This paper deals with a generalization of this line of research to the case of quasipolynomials that are entire functions which include both degree of the independent variable and exponential functions. The main objects of the paper are the developing of the concept of convex directions for quasipolynomials and exploiting this concept for construction of testing sets for quasipolynomial families. One of the primary sources of motivation for the class of problems considered in this paper is derived from process control. A typical problem formulation almost always includes a delay element in each subsystem process block. When we interconnect a number of such blocks in a feedback system, the study of robust stability involves quasipolynomials of the sort considered in this paper.

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 contribution an extension of the prediction-based design scheme proposed in Tsubakino et al. (2015) for compensation of input delays to the case of systems with input and state delays is presented. To derive safely implementable control laws we propose to apply additional input filters and obtain a closed-loop system in the form of a set of retarded type differential equations. An example illustrating the design scheme is given. [ABSTRACT FROM AUTHOR]

Abstract: In this contribution we present an extension of the prediction scheme proposed in Manitius and Olbrot (1979) for the compensation of the input delay to the case of linear systems with both input delay and state delay. For simplicity of the presentation we treat the case of systems with one state delay. [Copyright &y& Elsevier]

Abstract: A necessary and sufficient condition for the existence and uniqueness of Lyapunov matrices for neutral type single delay systems is presented. [Copyright &y& Elsevier]

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]