A variable gain impulsive observer for Lipschitz nonlinear systems with measurement noises. (English) Zbl 1504.93185
Summary: 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.
MSC:
| 93C27 | Impulsive control/observation systems |
| 93B53 | Observers |
| 93D23 | Exponential stability |
| 93D25 | Input-output approaches in control theory |
Keywords:
variable gain impulsive observer; Lipschitz nonlinear systems; exponential input-to-state stabilityReferences:
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