Discrete and intersample analysis of systems with aperiodic sampling

International audienceThis article addresses the stability analysis of linear time invariant systems with aperiodic sampled-data control. Adopting a difference inclusion formalism, we show that necessary and sufficient stability conditions are given by the existence of discrete-time quasi-quadratic Lyapunov functions. A constructive method for computing such functions is provided from the approximation of the necessary and sufficient conditions. In practice, this leads to sufficient stability criteria under LMI form. The inter-sampling behavior is discussed there: based on differential inclusions, we provide continuous-time methods that use the advantages of the discrete-time approach. The results are illustrated by numerical examples that indicate the improvement with regard to the existing literature

L-2 State Estimation With Guaranteed Convergence Speed in the Presence of Sporadic Measurements

This paper deals with the problem of estimating the state of a nonlinear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error whenever a new measurement is available. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve exponential convergence with a given decay rate of the estimation error. Robustness with respect to external perturbations and L2-external stability from plant perturbations to a given performance output are considered. Computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in an example

State observer with Round-Robin aperiodic sampled measurements with jitter

A sampled-data observer is proposed for linear continuous-time systems whose outputs are sequentially sampled via non-uniform sampling intervals repeating a prescribed Round-Robin sequence. With constant sampling intervals (jitter-free case) we provide constructive necessary and sufficient conditions for the design of an asymptotic continuous–discrete observer whose estimation error is input-to-state stable (ISS) from process disturbances and measurement noise. We use a time-varying gain depending on the elapsed time since the last measurement. With non-constant sampling intervals (jitter-tolerant case), our design conditions are only sufficient. A suspension system example shows the effectiveness of the proposed approach

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Stability Verification of Nearly Periodic Impulsive Linear Systems using Reachability Analysis

International audienceThe paper provides stability analysis to certain classes of hybrid systems, more precisely impulsive linear systems. This analysis is conducted using the notion of reachable set. The main contribution in this work is the derivation of theoretical necessary and sufficient conditions for impulsive linear systems with nearly periodic resets subject to timing contracts. This characterization serves as the basis of a computational method for the stability verification of the considered class of systems. In addition, we show how this work handles the problem of timing contract synthesis for the considered class and we generalize our approach to verify stability of impulsive linear systems with stochastic reset instants. Applications on sampled-data control systems and comparisons with existing results are then discussed, showing the effectiveness of our approach

Jump state estimation with multiple sensors with packet dropping and delaying channels

This work addresses the design of a state observer for systems whose outputs are measured through a communication network. The measurements from each sensor node are assumed to arrive randomly, scarcely and with a time-varying delay. The proposed model of the plant and the network measurement scenarios cover the cases of multiple sensors, out-of-sequence measurements, buffered measurements on a single packet and multirate sensor measurements. A jump observer is proposed that selects a different gain depending on the number of periods elapsed between successfully received measurements and on the available data. A finite set of gains is pre-calculated offline with a tractable optimisation problem, where the complexity of the observer implementation is a design parameter. The computational cost of the observer implementation is much lower than in the Kalman filter, whilst the performance is similar. Several examples illustrate the observer design for different measurement scenarios and observer complexity and show the achievable performance