A Non-Iterative Riccati Approach to Robust Control Design

In this paper we present a non-iterative procedure for designing a linear control law that guarantees practical stability of a system with matched additive disturbances and matched uncertainties in the system matrix and the input connection matrix. The solution of an algebraic Riccati equation is used to generate the feedback gains for a linear controller that guarantees asymptotic stability of the uncertain system without the additive disturbances. Then a multiplier which is a function of the magnitude of the additive disturbances is applied, and the resulting control guarantees practical stability. Unlike other Riccati approaches which require a search procedure, our approach leads directly to a control without requiring any iteration. Application of the results to tracking problems is discussed since formulation of the tracking problem for an uncertain system requires stabilization of a new system with additive disturbances.