Abstract In this paper, mechanical systems subject to impacts and contacts, that would be not controllable if the were absent (usually called jugglers ), are considered. On basis of an algorithm taken from literature a new procedure determine reference trajectory for such class systems, fully algorithmic procedure, able compute control input achieves dead–beat regulation “uncontrollable” subsystem just by using impacts, is given. Such exploits some tools borrowed algebraic geometry allow...

This paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events (switching systems). Parametric uncertainties are considered dimension state vector is allowed to vary among modes. To deal nature system, possible discontinuities its solutions at times, a properly amended control problem defined feedback law based on discontinuous version classical internal model principle proposed....

The problem of output regulation for a class hybrid linear systems characterized by periodic jumps is considered in this paper. Necessary and sufficient conditions its solution are provided both the full information error feedback case. By detailed analysis such conditions, several interesting properties derived, including fact that regulator must contain (suitably defined) copy flow zero dynamics plant addition to usual exosystem dynamics, generically solvable fat plants (having more inputs...

An infinitely rigid mass is considered, which moves on a plane under the action of proper control forces, within closed region delimited by an massive and circular barrier. A suitably amended tracking problem for class periodic trajectories, involving infinite number nonsmooth impacts between barrier, formally stated solved.

In this paper the problem of generating zero error steady-state responses is addressed for a class hybrid linear systems whose jumps are determined by time only. The procedure design an automatic device response and input described. Once such compensator ensuring incremental stability (see companion paper) available, classical output regulation same can be immediately solved. Compared with previously available results, no assumption needed on plant about minimum phaseness, relative degree or...

This paper reports some stabilization results for a class of hybrid linear systems whose jumps are determined by time only. Linearity the resulting closed-loop system implies that global asymptotic and incremental stability achieved at same time. In turn, allows solution recently considered output regulation problem coupling suitable steady state generator (described in companion paper) stabilizer from this paper. It is remarked general MIMO plants without relying on minimum phase, relative...

An infinitely rigid unitary mass (particle) is considered, moving on a planar region delimited by elliptical barrier (elliptical billiards) under the action of proper control forces. A class periodic trajectories, involving an infinite sequence non-smooth impacts between and at fixed times, found using LMIs based procedure. The jumps in velocities impact times render difficult (if not impossible) to obtain classical stability attractivity properties for dynamic system describing tracking...

The goal of this technical note is to design a switching signal estimator for class elementary continuous-time or switched systems. First, the system recast into polynomial form and, secondly, some tools borrowed from Algebraic Geometry are used express as function time derivatives output and input.

A complete procedure for the design of a robust output feedback regulator is proposed class uncertain linear hybrid systems with periodic jumps, using extension classical internal model principle. Simple conditions, testable on plant nominal data, problem solvability are given. The not restricted to be minimum phase, square, or single input output. has key feature containing an composed by two main units, flow model, in charge providing correct achieve regulation during flows, and jump...

Different input/output decoupling problems for a nonlinear model of high speed trains are studied. As it is natural in applications, the only one requirements, which to be obtained together with asymptotic stability and set point output regulation, presence constant disturbances.

Semi-invariants and relative characteristic functions extend to nonlinear systems the concept of eigenvector–eigenvalue pair for linear systems, are, therefore, very useful depict behaviour system. In this article, semi-invariants are used construct explicitly Lyapunov studying stability origin, continuous-time systems. Moreover, using well-known tools from differential geometry such as (orbital) symmetries, it is shown how can be found several classes Important connections with centre...

In this paper, a spinning and bouncing disk is used to illustrate some issues in regulation for class of hybrid systems. The use variables having clear physical meaning allows give nice interpretation the mechanism that can be used, fat plants, generate admissible trajectories.

This paper presents three novel methods for the multiobjective design of controllers with tunable parameters and fixed structure linear systems. These techniques exploit geometric properties varieties envelopes to obtain a closed-form expression set candidate Pareto optimal values. The objectives span from regional pole placement more general quadratic cost functionals, thus tackling wide variety control tasks. Examples applications proposed both (possibly, nonconvex) classical benchmark...

This paper is concerned with the concept of semi-invariant and its use for stability analysis origin nonlinear systems order two. Well known tools from differential geometry such as (orbital) symmetries render proposed results quite interesting a computational point view. The proper connections center manifold theory are pointed out.