Asynchronous Sampled-data Systems Research Articles

Novel Equalities for Stability Analysis of Asynchronous Sampled-Data Systems

This paper is concerned with the stability analysis problems of asynchronous sampled-data systems with use of a input-delay approach, where a sampled-data system can be reformulated into a time-delay system having incremental delays. For these systems, this paper introduces a new looped-functional to utilize both integral states and their interval-normalized ones. Utilization of these two types of integral state variables in a construction of stability conditions has been effective in reducing the conservatism. Further, generalized equalities are proposed for the case utilizing these two types of integral states. The sampled-data system formulation consists of a sampled state, a system state and its derivative. Here, the sampled state between two consecutive sampling instants is a constant value and thus can be eliminated by an integration with Legendre polynomials of positive degrees. Consequently, the system formulation turns into the equalities consisting of state variables, sampled-state variables, integral state variables and their interval-normalized ones without additional slack matrices. Based on the proposed equalities, a large computational burden can be reduced while reducing the conservatism. The effectiveness of the proposed approaches is demonstrated via three numerical examples for the stability analysis of asynchronous sampled-data systems.

Dynamic leader-following consensus for asynchronous sampled-data multi-agent systems under switching topology

This paper investigates the leader-following consensus problem for asynchronous sampled-data multi-agent systems with an active leader and under switching topology, in which the asynchrony means that each agent’s update actions are independent of the others’. First, the dynamic leader-following consensus problem for asynchronous sampled-data systems is transformed into the convergence problem of products of infinite general sub-stochastic matrices (PIGSSM), where the general sub-stochastic matrices are matrices with row sum no more than 1 but their elements are not necessarily nonnegative. We develop a method to cope with the corresponding convergence problem by matrix decomposition. In particular, we split the general sub-stochastic matrix into a sub-stochastic matrix which is a nonnegative matrix with row sum no more than 1, and a matrix with negative elements and row sum 0. Then based on a graphical approach and matrix analysis technique, we present a sufficient condition for the achievement of dynamic leader-following consensus in the asynchronous setting. Finally, simulation examples are demonstrated to verify the theoretical results.

Stability Criteria for Asynchronous Sampled-data Systems – A Fragmentation Approach

AbstractThe stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using a fragmentation technique inspired from recent advances in time-delay systems theory. The approach leads to a tractable convex feasibility problem involving a small number of finite dimensional LMIs. The approach is then finally illustrated through several examples.

Formula omitted]∞ and LQG control of asynchronous sampled-data systems

A class of dual-rate sampled-data systems is considered, where the sampling rate is asynchronously related to the rate at which the hold element is operating. Such asynchronous sampled-data systems are aperiodic, and hence the lifting technique, which is used to represent synchronous sampled-data systems as single-rate discrete systems, cannot be applied to the asynchronous case. In this study, optimal H ∞ and LQG controllers for asynchronous sampled-data systems are derived using a two-Riccati equation approach, which does not rely on the lifting method. A distribution theorem is used to evaluate the optimal stationary performance levels in the two cases.

Optimal H∞ and LQG Control of Asynchronous Sampled Data Systems

A class of dual-rate sampled-data systems is considered, where the sampling rate is asynchronously related to the rate at which the hold element is operating- Such asynchronous sampled-data systems are aperiodic, and hence the lifting technique, which is used to represent synchronous sampled-data systems as single-rate discrete systems, cannot be applied to the asynchronous case. In this study optimal H∞ and LQG controllers for asynchronous sampled-data systems are derived using a two-Riccati equation approach which does not rely on the lifting method. A distribution theorem is used to evaluate the optimal stationary performance levels in the two cases.