Kybernetika 34 no. 6, 681-691, 1998

Delay-dependent robust stability conditions and decay estimates for systems with input delays

Kostas Hrissagis and Olga I. Kosmidou


The robust stabilization of uncertain systems with delays in the manipulated variables is considered in this paper. Sufficient conditions are derived that guarantee closed-loop stability under state-feedback control in the presence of nonlinear and/or time-varying perturbations. The stability conditions are given in terms of scalar inequalities and do not require the solution of Lyapunov or Riccati equations. Instead, induced norms and matrix measures are used to yield some easy to test robust stability criteria. The problem of constrained control is also discussed, and alternative stability tests for the case of saturation nonlinearities are presented. Estimates of the transient behavior of the controlled system are also obtained. Finally, an example illustrates the results.