Stability of Switched Linear Discrete-Time Descriptor Systems with Explicit Calculation of a Common Quadratic Lyapunov Sequence

Abstract-In this paper, the stability of a switched linear regular descriptor system is considered. It will be shown that if a certain simultaneous triangularization condition on the subsystems is fulfilled and all the subsystems are stable then the switched system is stable under arbitrary switching. The result involves different descriptor matrices and extends to the singular case well-known results from the standard one. Furthermore, an explicit construction of a common Lyapunov sequence for a set of discrete-time regular linear descriptor subsystems is performed. The main novelty of the proposed approach is that the common Lyapunov sequence can be easily computed in comparison with previous works which either presented computationally-demanding methods or did not construct the common Lyapunov sequence explicitly

A Master-Slave Operating Technique for Material Removal Processes

This paper presents a master-slave operating technique for the material removal process aimed to be used for part prototyping. This system is designed for 5-axis milling processes which consist of a 6-DOF parallel haptic device as a master arm and a hybrid 5-axis H4 family parallel manipulator as a slave. According to the dissimilar structures between the master and slave, an operating technique to define positions and orientations of the slave’s end effecter or milling tool is applied in Cartesian space. Force reflection techniques in this work can help the operator move the master arm’s handle firmly along the virtual wall and generate significant feeling of force in master-slave milling tasks. The results of ball-end milling tasks show that each reproduced wooden work piece is similar to its referenced object with an average error of about 1 mm on each side and this master-slave operating technique can be used for dimensional scaling tasks

On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays

This paper investigates the causality properties of a class of linear time-delay systems under constant point delays which possess a finite set of distinct linear time-invariant parameterizations (or configurations) which, together with some switching function, conform a linear time-varying switched dynamic system. Explicit expressions are given to define pointwisely the causal and anticausal Toeplitz and Hankel operators from the set of switching time instants generated from the switching function. The case of the auxiliary unforced system defined by the matrix of undelayed dynamics being dichotomic (i.e., it has no eigenvalue on the complex imaginary axis) is considered in detail. Stability conditions as well as dual instability ones are discussed for this case which guarantee that the whole system is either stable, or unstable but no configuration of the switched system has eigenvalues within some vertical strip including the imaginary axis. It is proved that if the system is causal and uniformly controllable and observable, then it is globally asymptotically Lyapunov stable independent of the delays, that is, for any possibly values of such delays, provided that a minimum residence time in-between consecutive switches is kept or if all the set of matrices describing the auxiliary unforced delay—free system parameterizations commute pairwise.Ministerio de Educación (DPI2006-00714

Complex Formation Control of Large-Scale Intelligent Autonomous Vehicles

A new formation framework of large-scale intelligent autonomous vehicles is developed, which can realize complex formations while reducing data exchange. Using the proposed hierarchy formation method and the automatic dividing algorithm, vehicles are automatically divided into leaders and followers by exchanging information via wireless network at initial time. Then, leaders form formation geometric shape by global formation information and followers track their own virtual leaders to form line formation by local information. The formation control laws of leaders and followers are designed based on consensus algorithms. Moreover, collision-avoiding problems are considered and solved using artificial potential functions. Finally, a simulation example that consists of 25 vehicles shows the effectiveness of theory