ROBUST STABILIZATION OF TWIN-ROTOR MIMO PLANT

The problem of MIMO system robust stabilization is considered for the twin rotor MIMO system mechanical plant, where nonlinear dynamics and parametric uncertainties were considered as disturbances. The proposed control law consists of two components: the linear component homogenizes a closed-loop system with a chosen degree of homogeneity; the homogeneous component stabilizes the system asymptotically or in finite time depending on the degree of homogeneity. Due to homogeneity properties of the closed-loop system in the absence of disturbances, the synthesized control law ensures input-to-state stability of the closed-loop system. In comparison with other works, presented approach of control synthesis for twin rotor plant does not require the decomposition of the system and/or consideration of the cross-link effects as disturbances. To confirm the effectiveness of the presented results, an experimental approbation was carried out on the mechatronic plant

Robust Finite-time stability of homogeneous systems with respect tomultiplicative disturbances

International audienceLyapunov characterizations of output finite-time stability are presented for the system $x' = f (x), y = h(x)$ which is locally Lipschitz continuous out of the set $Y = {x ∈ R n : h(x) = 0}$ and continuous on $R^n$. The definitions are given in the form of $K$ and $KL$ functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples

Homogeneous Observer Design for Linear MIMO Systems

International audienceThe paper is devoted to the problem of state observation (particularly, in finite time) of linear MIMO systems. The presented nonlinear observer does not require system transformation to a canonical form and guarantees finite-time (asymptotic with a fixed-time attraction of any compact set containing the origin) stability of observation error equation if homogeneity degree is negative (positive). The proposed observer is robust in input-to-state sense with respect to disturbances and measurement noises. Performance of the observer is illustrated by a numerical example

On robustness of finite-time stability of homogeneous affine nonlinear systems and cascade interconnections

International audienceThis paper investigates robustness of finite-time stability property for a homogeneous nonlinear dynamical system with sufficiently small affine inputs. In addition, robust stability conditions are presented for the systems admitting homogeneous approximations at the origin or at infinity. The effects of additional stable unmodeled dynamics in the input channel on robust stability are investigated. The utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time-varying gains

Robustness of Homogeneous Systems with Respect to Time-Varying Perturbations

The problem of stability robustness with respect to time-varying perturbations of a given frequency spectrum is studied applyinghomogeneity framework. The notion of finite-time stability over time intervals of finite length, i.e. short-finite-time stability, isintroduced and used for that purpose. The results are applied to analyze the Super-Twisting algorithm behavior under sometime-varying perturbations, and to demonstrate some robustness properties of the three-tank system. Some simulation examplesillustrate these robustness properties

Analysis of scale invariance property applying homogeneity

International audienceThe problem of scalability of trajectories in homogeneous and locally homogeneous systems is considered. It is shown that the homogeneous systems have scalability property, and locally homogeneous systems possess this property approximately. The issue of closeness of trajectories for the system and its local homogeneous approximation is investigated. The notions of scale invariance and fold change detection are also studied. The results are illustrated by a cascade system analysis

Homogeneity Based Finite/Fixed-Time Observers for Linear MIMO Systems

International audienceThe paper is devoted to the problem of finite-time and fixed-time observation of linear multiple input multiple output control systems. The proposed dynamic observers do not require system transformation to a canonical form and guarantee convergence of the observation error to zero in a finite or in a fixed time. It is shown that the observers are robust (in input-to-state sense) against input disturbances and measurement noises. The results are supported with simulation examples

Robust finite-time output feedback stabilization of the double integrator

International audienceThe problem of finite-time output stabilization of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degrees of homogeneity) ensuring the finite-time stabilization. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. Robustness and effects of discretization on the obtained closed loop system are analyzed. The efficiency of the obtained solution is demonstrated in computer simulations

Design of a distributed finite-time observer using observability decompositions

International audienceIn this paper, a distributed observer is presented to estimate the state of a linear time-invariant plant in finite-time in each observer node. The design is based on a decomposition into locally observable and unobservable substates and on properties of homogeneous systems. Each observer node can reconstruct in finite-time its locally observable substate with its measurements only. Then exploiting the coupling, a finite-time converging observer is constructed for the remaining states by adding the consensus terms. A numerical example illustrates the result