Reduction of discrete-time two-channel delayed systems

In this letter, the reduction method is extended to time-delay systems affected by two mismatched input delays. To this end, the intrinsic feedback structure of the retarded dynamics is exploited to deduce a reduced dynamics which is free of delays. Moreover, among other possibilities, an Immersion and Invariance feedback over the reduced dynamics is designed for achieving stabilization of the original systems. A chained sampled-data dynamics is used to show the effectiveness of the proposed control strategy through simulations

Lyapunov stabilization of discrete-time feedforward dynamics

The paper discusses stabilization of nonlinear discrete-time dynamics in feedforward form. First it is shown how to define a Lyapunov function for the uncontrolled dynamics via the construction of a suitable cross-term. Then, stabilization is achieved in terms of u-average passivity. Several constructive cases are analyzed

ANALYSE ET COMMANDE DES SYSTEMES NON LINEAIRES NON COMMANDABLES EN PREMIERE APPROXIMATION DANS LE CADRE DE LA THEORIE DES BIFURCATIONS

CERGY-ENSEA (951272302) / SudocORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Linearization by Output Injection under Approximate Sampling

Linearization by output injection has been studied in both continuous time and discrete-time contexts. In this paper we discuss the possible preservation of such a property under sampling. It is shown that it can be maintained under approximate sampling up to the order of the system itself

Nonlinear average passivity and stabilizing controllers in discrete time

A novel notion of average passivity is proposed. On this basis, Passivity Based Controllers - PBC - such as the discrete-time versions of the well-known continuous-time negative output feedback and L(g)V controllers, are introduced and discussed

Accessibility under multirate control for nilpotent Lie algebra

The paper deals with the exact input-state matching under multirate sampled control of an input-affine dynamics under suitable nilpotency assumptions of the associated Lie algebra. Solutions are given under the assumption of nilpotency at the orders 1 and 2 and then at the order p under the additional assumption of nilpotency at order 1 of the zero-time controllability Lie algebra

From chronological calculus to exponential representations of continuous and discrete-time dynamics: A lie-algebraic approach

In this paper, formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived. It is shown that the chronological exponential admits an ordinary exponential representation, the exponent being given by an explicitly computable Lie series expansion. The results are then used to describe controlled dynamics, dynamics under sampling and forced discrete-time dynamics. The study emphasizes the role of Lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations, dynamics under sampling and forced discrete-time dynamics up to hybrid ones

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

International audienc

Nonlinear optimal stabilizing control under sampling

Starting from an optimal stabilizing controller designed for an input-affine continuous-time dynamics, the paper discusses the problem of computing a digital controller which preserves these properties under sampling. A direct digital approach which minimizes a modified cost functional is described. Some simulated examples illustrate the performances. © 2012 IEEE

Digital stabilization of delayed-input strict-feedforward dynamics

The paper deals with sampled-data stabilization of delayed input-affine dynamics. To remove the infinite dimensionality, the design is set in the sampled-data context and the delay is compensated with a discrete-time predictor. A simulated example illustrates the performances