Limits of stability and stabilization of time-delay systems. A small-gain approach (Q1650416)

The reviewed monograph is devoted to stability analysis and stabilization control design for time-delay systems. The operator-theoretic approach is used to derive stability conditions for linear time-invariant systems with time-varying delay and to study stabilization problem for linear systems subject to unknown variable delays. The proofs of the results are based on the classical small-gain theorems, which enable to employ a variety of methods from robust control theory. The fundamental limit of robust stabilization of time-delay system by the linear time-invariant controller is investigated. For this purpose, the notion of delay margin is generalized to the concept of delay radius, which indicates the admissible range of nonuniform, multivariate delays such that there exists a feedback controller capable of stabilizing the multi-input multi-output system. Finally, special attention is paid to the robust feedback stabilization of networked systems interconnected over lossy communication links and consensus problems for continuous-time multi-agent systems under delay. The interplay between the time-delay and the interconnection topology ensuring consensus is studied.