Mattia Mattioni

Sampled-Data Stabilization of Nonlinear Dynamics With Input Delays Through Immersion and Invariance

In this technical note, we show that Immersion and Invariance is a natural framework for the design of sampled-data stabilizing controllers for input-delayed systems. Assuming the existence of a continuous-time feedback in the delay free case, Immersion and Invariance stabilizability of the equivalent sampled-data dynamics is proven. The proof is constructive for the stabilizing controller. Two simulated examples illustrate the performances.

Immersion and invariance stabilization of strict-feedback dynamics under sampling

Abstract The paper deals with sampled-data stabilization of continuous-time dynamics in strict-feedback form via Immersion and Invariance. Starting from the characterization of the sampled-data target dynamics and its invariant manifold, a multi-rate control law is designed to achieve attractiveness and invariance of such a manifold. Simulations on an academic example and a practical case illustrate the performances.

Sampled-data stabilisation of a class of state-delayed nonlinear dynamics

The paper deals with the stabilisation of strict-feedback dynamics with a delay on the last component of the state. It is shown that the Immersion and Invariance approach provides a natural framework for solving the problem. An academic simulated example is provided.

Sampled-Data Reduction of Nonlinear Input-Delayed Dynamics

A reduction approach on the discrete-time equivalent model of a nonlinear input delayed system is proposed to design a sampled-data stabilizing feedback. Global asymptotic stability of the feedback system is so achieved by solving the problem over the reduction state. Stabilization of the reduced dynamics is obtained through input-Lyapunov matching. Connections with prediction-based methods are established. A simulated example illustrates the performances.

Stabilization of feedforward discrete-time dynamics through immersion and invariance

The paper deals with the problem of stabilizing discrete-time feedforward dynamics through Immersion and Invariance. Closed loop stabilization of the equilibrium is achieved making use of a passivity-based controller combined with a domination argument. A simulated example illustrates the performances.

Nonlinear discrete-time systems with delayed control: a reduction

In this work, the notion of reduction is introduced for discrete-time nonlinear input-delayed systems. The retarded dynamics is reduced to a new system which is free of delays and equivalent (in terms of stabilizability) to the original one. Different stabilizing strategies are proposed over the reduced model. Connections with existing predictor-based methods are discussed. The methodology is also worked out over particular classes of time-delay systems as sampled-data dynamics affected by an entire input delay.

Sampled-data stabilization of feedforward dynamics with Lyapunov cross-term

The paper addresses the problem of preserving the stabilizing performances of a continuous-time feedback under sampling. The discussion is developed with reference to a two-block feedforward system whose equilibrium is assumed globally stable. The design is passivity-based and exploits the construction of a Lyapunov function for the uncontrolled cascade.