Functional observers design for nonlinear discrete-time systems with interval time-varying delays

summary:This paper is concerned with the functional observer design for a class of Multi-Input Multi-Output discrete-time systems with mixed time-varying delays. Firstly, using the Lyapunov-Krasovskii functional approach, we design the parameters of the delay-dependent observer. We establish the sufficient conditions to guarantee the exponential stability of functional observer error system. In addition, for design purposes, delay-dependent sufficient conditions are proposed in terms of matrix inequalities to guarantee that the functional observer error system is exponentially stable. Secondly, we presented the sufficient conditions of the existence of internal-delay independent functional observer to ensure the estimated error system is asymptotically stable. Furthermore, some sufficient conditions are obtained to guarantee that the internal-delay independent functional observer error system is exponentially stable. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed method

Interval observers for continuous-time linear systems

International audienceWe consider continuous-time linear systems with additive disturbances and discrete-time measurements. First, we construct an observer, which converges to the state trajectory of the linear system when the maximum time interval between two consecutive measurements is sufficiently small and there are no disturbances. Second, we construct interval observers allowing to determine, for any solution, a set that is guaranteed to contain the actual state of the system when bounded disturbances are present

Interval Estimation for Linear Switched System

International audienceIn this paper, the problem of state estimation is investigated for linear switched system, a subclass of hybrid systems. It will be shown that the interval observer is very often exists under moderate conditions at least in discrete time instants from continuous-time measurements. The novelty consists in proposing new conditions of cooperativity for switched systems in discrete time instants, which guarantee errors nonnegativity of interval observation. The efficiency of the interval observers is shown through simulation examples

On Design of Interval Observers with Sampled Measurement

International audienceNew design of interval observers for continuous-time systems with discrete-time measurements is proposed. For this purpose new conditions of positivity for linear systems with sampled feedbacks are obtained. A sampled-data stabilizing control is synthesized based on provided interval estimates. Efficiency of the obtained solution is demonstrated on examples

Event-Triggered Control for Discrete-Time Systems Using a Positive Systems Approach

International audienceWe provide an output feedback eventtriggered controller for discrete-time linear systems. We make novel use of positive systems, interval observers, an event-triggered state estimator, and triggering times that are computed from estimator values. This provides a discrete-time analog of our recent positive systems approach for continuous-time systems. A key novel ingredient in our discrete-time event triggers is their use of vectors of absolute values, instead of the usual Euclidean norm. We illustrate the benefits of our method using a model for event-triggered BlueROV2 underwater vehicles

New Fixed Time and Fast Converging Reduced Order Observers

International audienceFor nonlinear continuous-time systems with continuous measurements of the output, we provide new reduced order observers that converge in finite time. The convergence time is independent of the initial state. For cases where the measurements are discrete, we provide asymptotically converging observers, whose rate of convergence is proportional to the negative of the logarithm of the size of the sampling interval. Our observers are based on the observability Gramian

Design of Interval Observers for Estimation and Stabilization of Discrete-Time LPV Systems

International audienceThis work is devoted to interval observers design for discrete-time Linear Parameter-Varying (LPV) systems under the assumption that the vector of scheduling parameters is not available for measurements. Two problems are considered: a pure estimation problem and an output stabilizing feedback design problem where the stability conditions are expressed in terms of Linear Matrix Inequalities (LMIs). The efficiency of the proposed approach is demonstrated through computer simulations

Observer synthesis under time-varying sampling for Lipschitz nonlinear systems

International audienceIn this work, the problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements is considered. This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation. Since the network introduces variations in the sampling time, the observer must be designed so that it takes them into account. Here impulsive observers, which make instantaneous correction when information is received, are investigated. Moreover, we consider time-varying observer gains adapting to the varying sampling interval. In order to deal with both continuous-time and discrete-time dynamics, a new hybrid model is used to state the problem and establish the convergence of the proposed observer. First, generic conditions are provided using a hybrid Lyapunov function. Then, a restriction of the generic Lyapunov function is used to establish tractable conditions that allows the analysis and synthesis of an impulsive gain

New Bounds for State Transition Mat.

International audienceWe address the problem of constructing matrix-valued interval observers for estimating state transition matrices for time-varying systems. We provide less conservative estimators than those in recent literature. We cover continuousand discrete-time linear systems, under Metzler or nonnegativity conditions on the coefficient matrices. We show how to satisfy our Metzler conditions after simple changes of coordinates. We illustrate our method using a feedback stabilized underwater marine robotic dynamics with unknown control gains