Stability performance robustness of uncertain time-varying systems

An optimization scheme for robust stability performance of linear time-varying systems with uncertainties in the state and the control matrices is used to derive new results in which the rates of change of the time-varying structured uncertainties are explicitly expressed. While known conditions on the stabilizing controllers are imposed, stability requires the existence of a positive definite solution of an auxiliary Riccati equation has been revealed, confirming the known condition that calls for the existence of a positive definite solution of the conventional matrix Riccati equation. An illustrative example is included.