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This paper investigates the variable gain impulsive observer design problem for Lipschitz nonlinear systems. It is assumed that the measurements are contaminated by noise and received by observer at aperiodic instants. To establish a tractable design condition for impulsive observers, the piecewise linear interpolation method is used to construct the variable gain function. To quantify the impact of the measurement noises and exogenous disturbance on the estimation error, a Lyapunov-based condition for establishing exponential input-to-state stability (EISS) property of the observation error dynamics is presented. Then it is shown that the EISS condition can be expressed as a set of linear matrix inequalities (LMIs) by introducing a piecewise quadratic Lyapunov function. A convex optimization problem is proposed in which the EISS gain is minimized. Comparisons with the existing methods show the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

The finite hybrid L 1 × l 1 -gain problem for T-S fuzzy positive impulsive systems is proposed. The problem is solved in the framework of discretized copositive Lyapunov functions. In order to highlight the effect of interaction between continuous and discrete dynamics on system performance, both the impulse state and the discrete-time input are included in the introduced copositive Lyapunov functions. By selecting appropriate auxiliary functions for adjusting the variation of copositive Lyapunov function at impulse instants, the introduced copositive Lyapunov functions turn out to be continuous along the solutions of the system. Through employing the novel discretized function, new criteria for exponential stability and finite hybrid L 1 × l 1 -gain are derived in terms of finite linear programming. Numerical examples show that the new criteria can achieve higher accuracy than those of the existing ones. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear time-delay system with delayed impulses and external disturbances is considered. The robustness problem of L p -stability with respect to impulse-delays is addressed. In order to circumvent the technical difficulties caused by delayed impulses, the impulses-delayed system is modeled as an impulse-delay free system with switching impulses by means of an augmentation method. Based on the switching structure of the augmented system, a time-dependent Lyapunov function is constructed from the original Lyapunov function for the impulse-delay free case. Then by employing the new designed Lyapunov function combined with the use of Razumikhin-type arguments, sufficient conditions for exponential stability and L p -stability are derived. The developed results characterize the relationship among the impulse intervals, the size of impulse-delays, and the level of L p -gain. Two numerical examples are presented to illustrate the effectiveness of the developed methodology. [ABSTRACT FROM AUTHOR]

The robust control problem of a class of uncertain systems subject to intermittent measurement as well as external disturbances is considered. The disturbances are supposed to be generated by an exogenous system, while the state information is assumed to be available only on some nonoverlapping time intervals. A composite design consisting of an intermittent state feedback controller augmented by a disturbance compensation term derived from a disturbance observer is formulated. Unlike the conventional disturbance observers, the proposed disturbance observer is modelled by a switched impulsive system, which makes use of the intermittent state data to estimate the disturbances. Stability analysis of the resulting closed-loop system is performed by applying a piecewise time-dependent Lyapunov function. Then a sufficient condition for the existence of the proposed composite controllers is derived in terms of linear matrix inequalities (LMIs). The controller and observer gains can be achieved by solving a set of LMIs. Further, a procedure to limit the norms of the controller and observer gains is given. Finally, an illustrative example is presented to demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]