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Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions. (English) Zbl 1078.93054
Summary: This paper considers the problem of robust stability for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. Both delay-independent and delay-dependent stability conditions are characterized by linear matrix inequalities which allow the use of parameter-dependent Lyapunov functionals to analyse the system stability against parameter perturbations, and therefore improve the conservativeness resulting from the single Lyapunov functional. In order to determine the maximum of time-delay within which the system remains stable, the problem can be cast into a generalized eigenvalue problem and solved by standard LMI solvers. Two examples are included to illustrate the proposed method.
93D09Robust stability of control systems
93C23Systems governed by functional-differential equations