Section: New Results

Non-linear, Sampled and Time-delay systems

Nonlinearities, sampling, quantization and time-delays cause serious obstructions for control and observer design in many fields of techniques and engineering (e.g. networked and internet systems, distributed systems etc.). The proposed by the team algebraic approach suits well for estimation and regulation in such a type of systems. The recent results are listed below:

• The work [59] aims at decreasing the number of sampling instants in state feedback control for perturbed linear time invariant systems. The approach is based on linear matrix inequalities obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments that guarantee the exponential stability for a chosen decay-rate.

• A novel self-triggered control, which aims at decreasing the number of sampling instants for the state feedback control of perturbed linear time invariant systems, has been proposed in [60] . The approach is based on convex embeddings that allow for designing a state-dependent sampling function guaranteeing the system's exponential stability for a desired decay-rate and norm-bounded perturbations. One of the main contributions of the paper [60] is an LMI based algorithm that optimizes the choice of the Lyapunov function so as to enlarge the lower-bound of the sampling function while taking into account both the perturbations and the decay-rate.

• In [63] , we consider the issue of stabilizing a class of linear systems using irregular sampled output measurements.

• The paper [73] is dedicated to the stability analysis of nonlinear sampled-data systems, which are affine in the input. Assuming that a stabilizing continuous-time controller exists and it is implemented digitally, we intend to provide sufficient asymptotic/exponential stability conditions for the sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling periods. The stability analysis problem is formulated both globally and locally. The main idea of the paper is to address the stability problem in the framework of dissipativity theory. Furthermore, the result is particularized for the class of polynomial input-affine sampled-data systems, where stability may be tested numerically using sum of squares decomposition and semidefinite programming.

• The problem of output control design for linear system with unknown and time-varying input delay, bounded exogenous disturbances and bounded deterministic measurement noises has been considered in [77] . The prediction technique has been combined with Luenberger-like observer design in order to provide the stabilizing output feedback. The scheme of parameters tuning for reduction of measurement noises effect and exogenous disturbances effects has been developed using the Attractive Ellipsoids Method.

• Using the theory of non-commutative rings, the paper [39] studies the delay identification of nonlinear time-delay systems with unknown inputs. A sufficient condition has been given in order to deduce an output delay equation from the studied system. Then necessary and sufficient conditions have been proposed to judge whether the deduced output delay equation can be used to identify the delay, which is involved in this equation.