Impulsive observer-based control for linear systems using irregularly sampled measurements

Abstract

In this paper, we consider the issue of stabilizing a class of linear systems using irregular sampled output measurements. For this purpose, we design a standard linear state feedback controller and an impulsive observer to provide an estimate the non-measured states, which are subsequently fed back in the control algorithm. We consider linear systems that can be decomposed, via a change of coordinates, into their respective measured and unmeasured dynamics. We consider the two cases whereby the unmeasured subspace is stable and unstable respectively. In the case where the unmeasured subspace is stable, we employ a standard impulsive observer coupled with a continuous linear feedback control. Next, when the unmeasured subspace is unstable, we employ two cascaded observers-an impulsive and a Luenberger observer-in conjunction with a linear feedback control. In order to prove the stability of the overall closed-loop system we proposed a practical stability result for a class of linear impulsive systems. Some simulation results are presented to show the performance of the observer-based control. Finally, some conclusions are drawn.

Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers

“…In any case, the fact that the continuous dynamics of (16) do not contain such a forcing term is the main advantage of the proposed impulsive observer. In fact, the absence of a forcing term y.t s / O y.t/ in the dynamics of O x implies that also the error dynamics (18) do not contain such a term. This last term, if present, would force the error dynamics, possibly determining a divergence, and has to be appropriately dominated in the stability analysis (conducted in the following by a Lyapunov function).…”

“…Let us consider the system (1), with .A; C / observable and satisfying (2). Under the same hypotheses and notations of Theorem 4.1, the observer (16), with the event-triggering condition (17), and the gain G D P 1 1 P 3 , ensures that the origin of error dynamics (18), (19) globally practically converge to the set…”

“…Recently, impulsive observers for continuous‐time systems have been proposed , and, using discontinuous Lyapunov functions, sufficient conditions for the existence of these observers have been derived in terms of linear matrix inequalities (LMIs). Further recent developments in the design of impulsive observers can be found in for linear systems and in for nonlinear ones. Impulsive observer dynamics are described by impulsive differential equations, with the observer state updated only at discrete instants.…”

Observer-Based Impulsive Controller Design for Treatment of Hepatitis C Disease

“…The unavailability of system states because of the technical limitations or high prices of measuring devices is a problem in the controller design. Observers have been designed in order to estimate the unmeasured states of linear and nonlinear systems, − and they have also been used for several biological applications. − Impulsive observers have been proposed to estimate the unknown states of the system when the output measurements are only available at special discrete times. , Since, in the HCV treatment process, the viral load is measured at certain sampling times, an impulsive observer should be designed to estimate the unknown states for implementation of the treatment strategy. For this purpose, the impulsive Luengerger-like observer, which has been extensively utilized for the nonlinear systems, has been chosen.…”

“…36−39 Impulsive observers have been proposed to estimate the unknown states of the system when the output measurements are only available at special discrete times. 40,41 Since, in the HCV treatment process, the viral load is measured at certain sampling times, an impulsive observer should be designed to estimate the unknown states for implementation of the treatment strategy. For this purpose, the impulsive Luengerger-like observer, which has been extensively utilized for the nonlinear systems, has been chosen.…”