Alexandre Seuret

Corentin Briat, Alexandre Seuret

A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwell-times results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampled-data systems, illustrate the efficiency of the approach.

Corentin Briat, Alexandre Seuret

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve non-monotonically along the flow of the system in a new way, broadening then the admissible class of systems which may be analyzed. As a byproduct, the particular structure of the obtained conditions makes the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach.

Corentin Briat, Alexandre Seuret

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach.

Corentin Briat, Alexandre Seuret

Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous works on the analysis of sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterization of their associated discrete-time stability conditions. We prove here that these conditions are also \necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases.

Qian Feng, Sing Kiong Nguang, Alexandre Seuret

In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay terms under consideration can contain any $\fL^{2}$ functions which are approximated via a class of elementary functions which includes the option of Legendre polynomials. By using this broader class of functions compared to the existing Legendre polynomials approximation approach, one can construct a Liapunov-Krasovskii functional which is parameterized by non-polynomial functions . Furthermore, a novel generalized integral inequality is also proposed to incorporate approximation error in our stability (dissipativity) conditions. Based on the proposed approximation scenario with the proposed integral inequality, sufficient conditions determining the dissipativity and stability of a CDDS are derived in terms of linear matrix inequalities. In addition, several hierarchies in terms of the feasibility of the proposed conditions are derived under certain constraints. Finally, several numerical examples are presented in this paper to show the effectiveness of our proposed methodologies.

Gerson Portilla, Carolina Albea, Alexandre Seuret

Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result relies on a prediction scheme considering nominal system parameters. By constructing a Lyapunov function that considers the prediction error, we demonstrate the exponential convergence of the system trajectories and system prediction to a robust limit cycle. An example is provided to validate the obtained result.