Stabilization of uncertain linear distributed delay systems with dissipativity constraints

Abstract

This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials, trigonometric and exponential functions. By constructing a Liapunov-Krasovski\v{i} functional related to the distributed kernels, sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities (LMIs). In contrast to existing methods, the proposed scenario is less conservative or requires a smaller number of decision variables based on the application of a newly derived integral inequality. Finally, numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology.