Abstract
A nonlinear Lur’e-type plant with a sector bound nonlinearity is considered. The plant is stabilized by a discrete-time feedback signal with a nonperiodic uncertain sampling. The sampling control function is nonlinear and also obeys some sectoral constraints at discrete (sampling) times. The linear matrix inequality (LMI) conditions for the stability of the closed-loop system are obtained.
Highlights
Absolute stability theory of nonlinear systems with sectoral constraints goes back to works of A
The advantage of the Linear Matrix Inequalities (LMIs) approach to different problems of applied mathematics was comprehensively discussed in monograph [5] that launched a broad development of a specific computer software for exploring LMIs
This paper aims to demonstrate how the classical absolute stability technique (Yakubovich’s S-procedure, Lur’e sectoral constraints, integral-quadratic constraint (IQC), and Gelig’s discrete-time constraints) can be applied to stability analysis of a nonlinear Lur’e-type plant under a sampled-data nonlinear stabilizing signal
Summary
Absolute stability theory of nonlinear systems with sectoral constraints goes back to works of A. The main idea of the Gelig’s approach is a substitution of the initial train of pulses for a sequence of the average values of these pulses, with a supposition that these averages satisfy some instant constraints The errors of such a substitution are estimated with the help of IQCs. Unlike other averaging theorems, the results of Gelig were not asymptotical, but Mathematical Problems in Engineering could be used for an estimation of the sampling frequency from below. The problem of stabilization of a continuous-time plant by a sampled-data signal attracted much attention last decade; see a review paper [27] where the existing modern approaches are outlined. This paper aims to demonstrate how the classical absolute stability technique (Yakubovich’s S-procedure, Lur’e sectoral constraints, IQCs, and Gelig’s discrete-time constraints) can be applied to stability analysis of a nonlinear Lur’e-type plant under a sampled-data nonlinear stabilizing signal. The main result is illustrated by an application to a simple first-order problem and to a sampled-data control of a mathematical pendulum
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