Section: New Results

Non-Linear, Sampled-Data And Time-Delay Systems

• The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced in [39] . Theorems on Lyapunov, asymptotic, (hyper) exponential , finite-time and fixed-time stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is presented.

• A recent generalization of the classical ISS theory to multistable systems is presented in [17] . Based on it a robust synchronization protocols with respect to a compact invariant set of the unperturbed system are designed in [14] , [49] .

• The paper [21] deals with the design of an active fault-tolerant control strategy based on the supervisory control approach technique for linear time invariant MIMO systems affected by disturbances, measurement noise, and faults. From a bank of Luenberger observers that plays the role of a fault detection and isolation scheme, the supervisory algorithm selects the suitable fault-tolerant controller by means of a hysteresis-based switching mechanism based on the method proposed in this paper.

• In [30] motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback [55] .

• The work [31] aims at enlarging the sampling intervals in several state feedback control situations by designing a sampling map in the state space. For linear time invariant (LTI) systems with state-bounded perturbations this guarantees exponential stability with a chosen decay-rate. The approach is based on linear matrix inequalities (LMIs) obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments. Then, the obtained results are extended to design the sampling map in three dynamic sampling control situations: event-triggered control, self-triggered control, and state-dependent sampling.

• In the paper [43] the problem of discrete and continuous state estimation for a class of uncertain switched LPV systems is addressed. Parameter identification techniques are applied to realize an approximate identification of the scheduled parameters of a switched LPV system with certain uncertainties and/or disturbances. A discrete state estimation is achieved using the parameter identification. A Luenberger-like hybrid observer, based on discrete state information and LMIs approach, is used for the continuous state estimation.

• The paper [70] contributes to the exponential stability analysis for impulsive dynamical systems based on a vector Lyapunov function and its divergence operator. The method relies on a 2D time domain representation. The results are applied to analyze the exponential stability of linear impulsive systems based on LMIs.