Maximum Allowable Sampling Period Research Articles

Estimation of Sampling Period for Stochastic Nonlinear Sampled-Data Systems With Emulated Controllers

This note focuses on determining the value of the maximum allowable sampling period (MASP) that guarantees the stability of stochastic nonlinear sampled-data systems with emulated controllers. Two methods are proposed to compute MASP, one based on sufficient Lyapunov-like conditions on stabilization of stochastic nonlinear systems in mean square and the other from applying Barbalat's Lemma. Comparison studies are made and illustrated for the two methods by a numerical example.

A characterization of integral input-to-state stability for hybrid systems

This paper addresses characterizations of integral input-to-state stability (iISS) for hybrid systems. In particular, we give a Lyapunov characterization of iISS unifying and generalizing the existing theory for pure continuous-time and pure discrete-time systems. Moreover, iISS is related to dissipativity and detectability notions. Robustness of iISS to sufficiently small perturbations is also investigated. As an application of our results, we provide a maximum allowable sampling period guaranteeing iISS for sampled-data control systems with an emulated controller.

Exponential Stability Analysis of Sampled-Data ODE–PDE Systems and Application to Observer Design

A small-gain approach is presented for analyzing exponential stability of a class of (dynamical) hybrid systems. The systems considered in the paper are composed of finite-dimensional dynamics, represented by a linear ordinary differential equation (ODE), and infinite-dimensional dynamics described by a parabolic partial differential equation (PDE). Exponential stability is established under conditions involving the maximum allowable sampling period (MASP). This new stability result is shown to be useful in the design of sampled-output exponentially convergent observers for linear systems that are described by an ODE–PDE cascade. The new stability result also proves to be useful in designing practical approximate observers involving no PDEs.

Continuous output feedback stabilization for nonlinear systems based on sampled and delayed output measurements

SummaryThis paper addresses the problem of output feedback stabilization for nonlinear systems with sampled and delayed output measurements. Firstly, sufficient conditions are proposed to ensure that a class of hybrid systems are globally exponentially stable. Then, based on the sufficient conditions and a dedicated construction continuous observer, an output feedback control law is presented to globally exponentially stabilize the nonlinear systems. The output feedback stabilizer is continuous and hybrid, and can be derived without discretization. The maximum allowable sampling period and the maximum delay are also given. At last, a numerical example is provided to illustrate the design methods. Copyright © 2015 John Wiley & Sons, Ltd.

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

ABSTRACTThis paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.

Synchronization of a class of nonlinear multi-agent systems with sampled-data information

The synchronization problem for a class of nonlinear multi-agent systems only using sampled-data information is investigated in this paper. The multi-agent system has a leader–follower architecture, and the desired synchronization state is the leader’s state, which is available to only a subset of the follower agents. First, by integrating the graph theory and Lyapunov design methods together, a sampled-data control law is designed. Then, the explicit formula for the maximum allowable sampling period is computed to guarantee states synchronization for all agents. An example is given to verify the efficiency of the proposed method.

Sampled-Data Piecewise Affine Differential Inclusions

This paper addresses exponential stability and stabilization of sampled-data piecewise affine differential inclusions (PWADI) with an unknown nonuniform sampling rate. The contributions of this paper are threefold. First, given a controller, sufficient conditions for exponential stability of closed-loop sampled-data PWADI are presented using a piecewise smooth Krasovskii functional. Second, assuming the controller is piecewise linear and the Krasovskii functional is piecewise quadratic, the stability conditions are cast as linear matrix inequalities (LMIs). Third, sufficient conditions for sampled-data controller synthesis for PWADI are formulated in terms of LMIs, with the maximum allowable sampling period as a parameter. The effectiveness of the approach is shown via a PWADI example that is motivated by a nonlinear system.

Distributed formation control of 6-DOF autonomous underwater vehicles networked by sampled-data information under directed topology

In this paper, a sampled-data networking strategy is investigated for the formation problem of multiple 6-DOF autonomous underwater vehicles (AUVs) in the presence of external disturbances. Unlike the common condition in most literatures associated with multiple vehicles, where the information is assumed to be exchanged continuously, in our proposed strategy, the position and orientation information of the multiple AUVs is exchanged according to a discrete-time sequence, which is more applicable to current technologies for underwater communications. More precisely, this strategy can be modeled by a sample-and-hold mechanism and is capable of both uniform and non-uniform sampling cases. In particular, it has a potential advantage from an energy perspective, since communication reduction always leads to less energy consumption. By model transformation, distributed controllers are designed based on input-to-state stability (ISS) property to ensure that both configuration formation and rendezvous-type formation can be achieved. An optimization procedure is also presented to calculate the maximum allowable sampling period. Finally, a numerical example is provided to illustrate the effectiveness and applicability of the theoretical results.

Global synchronization of nonlinear coupled complex dynamical networks with information exchanges at discrete-time

This paper studies the problem of synchronization for a class of complex networks with discrete-time couplings. The intrinsic local dynamical behaviors of the nodes in the complex networks are varied continuously while the manners of information interaction between every two different nodes are discrete time-varying rather than proceeded continuously, that is, the communications of the nodes only active at some discrete instants. Similar to the sampled data control systems, we convert the discrete time coupling issue into an effective time-varying delayed coupling network. By constructing the Lyapunov function skillfully, sufficient conditions are derived to guarantee the realization of the synchronization pattern for all initial values based on the Lyapunov stability theorem and linear matrix inequalities. What is more, the maximum allowable sampling period for communication is obtained through a optimization problem. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

Sampled-Data Consensus for High-Order Multiagent Systems under Fixed and Randomly Switching Topology

This paper studies the sampled-data based consensus of multiagent system with general linear time-invariant dynamics. It focuses on looking for a maximum allowable sampling period bound such that as long as the sampling period is less than this bound, there always exist linear consensus protocols solving the consensus problem. Both fixed and randomly switching topologies are considered. For systems under fixed topology, a necessary and sufficient sampling period bound is obtained for single-input multiagent systems, and a sufficient allowable bound is proposed for multi-input systems by solving theH∞optimal control problem of certain system with uncertainty. For systems under randomly switching topologies, tree-type and complete broadcasting network with Bernoulli packet losses are discussed, and explicit allowable sampling period bounds are, respectively, given based on the unstable eigenvalues of agent’s system matrix and packet loss probability. Numerical examples are given to illustrate the results.

Global Stabilization of a Class of Inherently Nonlinear Systems under Sampled-data Control

For a class of inherently nonlinear systems with uncertain parameters, the global stabilization problem via sampled-data control is investigated in this paper. First of all,based on the technique of adding a power integrator and a recursive argument, a class of sampled-data state feedback controllers are proposed. Then under the proposed controller, by using a suitable Lyapunov functional, it is shown that there is a maximum allowable sampling period which can guarantee the global asymptotical stability of the closed-loop system. Since the proposed controller is discrete-time, it can be easily implemented by computers. Finally, an example is given to verify the efficiency of the proposed method.

Continuous-Discrete Observer for State Affine Systems With Sampled and Delayed Measurements

The observation of a class of multi-input multi-output (MIMO) state affine systems with both sampled and delayed output measurements is addressed. These two constraints disturb simultaneously the convergence of the observer. Assuming some persistent excitation conditions to hold, and by using Lyapunov tools adapted to impulsive systems, two classes of global exponential observers are proposed. Some explicit relations between maximum allowable delay and maximum allowable sampling period are given. An extension to some classes of nonlinear systems is also given.

Stochastic Bounded Consensus Tracking of Second-Order Multi-Agent Systems with Measurement Noises and Sampled-Data

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state, and the measurements are corrupted by random noises. The probability limit theory, the algebra graph theory, and some other techniques are employed to derive the necessary and sufficient condition guaranteeing the mean square bounded consensus tracking. It turns out that the maximum allowable sampling period depends on not only the network topology but also the constant feedback gains. Furthermore, the effects of the sampling period on tracking performance, including the tracking speed and the static tracking error, are also analyzed. The results show that reducing the sampling period can accelerate the tracking speed and decrease the static tracking error. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Global stabilization of a class of uncertain upper‐triangular systems under sampled‐data control

SUMMARYThis paper considers the problem of using a sampled‐data controller to globally stabilize a class of uncertain upper‐triangular systems. First, we design a continuous‐time controller by integrating the nested saturation and Lyapunov design methods together. Then, the explicit formula for the maximum allowable sampling period is computed such that the discretized controller will guarantee global stability and robustness against uncertainties of the closed‐loop system. The bound of a proposed sampled‐data controller can be adjusted to any small level to accommodate the actuation bound in practical implementation. Copyright © 2012 John Wiley & Sons, Ltd.

Global Stabilization of Feedforward Systems Under Perturbations in Sampling Schedule

For nonlinear systems that are known to be globally asymptotically stabilizable, control over networks introduces a major challenge because of the asynchrony in the transmission schedule. Maintaining global asymptotic stabilization in sampled-data implementations with zero-order hold and with perturbations in the sampling schedule is not achievable in general, but we show in this paper that it is achievable for the class of feedforward systems. We develop sampled-data feedback stabilizers which are not approximations of continuous-time designs but are discontinuous feedback laws that are specifically developed for maintaining global asymptotic stabilizability under any sequence of sampling periods that is uniformly bounded by a certain „maximum allowable sampling period.”

Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems

The purpose of this note is to apply recent results on stabilization of networked control systems to obtain an explicit formula for the maximum allowable sampling period (MASP) that guarantees stability of a nonlinear sampled-data system with an emulated controller. Such formulas are of great value to control practitioners.