Luca Zaccarian

We propose a decentralized stubborn observer architecture for linear time-invariant (LTI) systems. Partitioning the outputs into blocks with individual adaptive thresholds isolates measurement corruptions and prevents their propagation. By mapping the system into a lower block-triangular form, we prove global exponential stability (GES) in the disturbance-free case. Moreover, we establish Input-to-State Stability (ISS) to output disturbances and exact cancellation of impulsive outliers under relaxed block-wise dwell-time conditions. Numerical simulations on a vehicle platoon illustrate the improved robustness compared with centralized designs.

We establish sufficient conditions for positive (semi-)definiteness, with or without radial unboundedness, for nonquadratic Lyapunov function constructed as sign-indefinite quadratic forms involving the state and the deadzone of a suitable input. We then use these conditions to build weak nonquadratic Lyapunov functions establishing global asymptotic stability of linear systems in feedback through a saturation, leveraging invariance principles. Our results are shown to be non-conservative (necessary and sufficient) for a family of well known prototypical examples of linear SISO feedbacks that are not globally exponentially stabilizable (the so-called ANCBI plants). Our multi-input extension leads to convex stability analysis tests, formulated as linear matrix inequalities that are applicable to ANCBI non-globally-exponentially-stabilizable plants.

State estimation is crucial for control and monitoring of dynamical systems, but sporadic disturbances (outliers) can severely degrade the estimator's performance. This paper studies the stability of a so-called "stubborn" observer, designed to mitigate the effects of outliers, for discrete-time linear systems. We prove that the detectability of the system is both necessary and sufficient for global exponential stability of the observer, providing an improvement over existing results that rely on potentially infeasible LMI conditions. The proof is constructive, leading to practical guidelines for selecting the observer parameters. Numerical simulations demonstrate the observer's effectiveness in mitigating outliers and its superior performance compared to a classical Luenberger observer.

In this paper, we propose discontinuous control laws to globally stabilize a target position of a hovercraft. Equations of motion of the hovercraft are derived through a kinematic model approximation of a dynamic model taken from the literature. Discontinuous feedback laws for the kinematic and the dynamic model are derived and analyzed using a hybrid systems formulation of the closed-loop dynamics. Numerical simulations confirm the theoretical convergence guarantees and validate the kinematic model as a valid simplification of the dynamic model.

In this paper, we investigate the problem of synchronization of multi-agent systems described by hybrid non-linear input affine dynamics. We consider networks described by undirected connected graphs without leader. We present a set of sufficient conditions based on an LMI approach in order to design a state-feedback distributed control law. Then, by exploiting the properties of the graph incidence matrix we provide an optimization of the tuning parameters. The incidence matrix properties also allow us to construct a Lyapunov function to establish synchronization of the hybrid network.

We propose a robustly stabilizing Lyapunov-based control scheme for a Multi-Input Converter using a Nonlinear Disturbance Observer for the load current estimation. The closed-loop system ensures an output voltage regulation and eliminates the requirement of knowing the current load, thus mitigating the impact of current fluctuations, without relying on typically inaccessible or impractical measurements. Robust asymptotic stability is guaranteed by Lyapunov theory. The main result is validated by simulations and experiments.

In this paper we propose novel global and regional stability analysis conditions based on linear matrix inequalities for a general class of recurrent neural networks. These conditions can be also used for state-feedback control design and a suitable optimization problem enforcing H2 norm minimization properties is defined. The theoretical results are corroborated by numerical simulations, showing the advantages and limitations of the methods presented herein.

A stabilizing controller design for linear systems subject to asymmetric actuator saturation is proposed. Stabilization is achieved by focusing on shifted equilibria selected via the solution of an optimization problem ensuring convergence to the origin of the shifted equilibrium. To enable the computational time required by the optimizer, we impose sampled-data updates of the shifted equilibria and cast our description within a hybrid dynamical systems formulation. Two feedback solutions are given, using exact and inaccurate optimization algorithms, thus establishing interesting tradeoffs between continuous-time dynamics and computationally expensive iterative discrete-time parametric optimization schemes. Through numerical examples, estimates of the region of attraction obtained through the method outlined in this article are compared to other methods in literature. In addition, the real-time applicability of the control law is illustrated on numerical examples.