Low-and-high gain design technique for linear systems subject to input saturation-a direct method

The low-and-high gain design technique, which was initiated for a chain of integrators and completed for general linear asymptotically null controllable with bounded controls systems, was conceived for semiglobal control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capacity and semi-global disturbance rejection. Although the low-and-high gain design technique as initiated for a chain of integrators is based on an explicit eigenstructure assignment algorithm, its full development is based on the solution of an algebraic Riccati equation (ARE) which is parameterized in an arbitrarily small scalar, called low gain parameter. In this paper, we develop a new complete low-and-high gain design procedure which is based on an explicit eigenstructure assignment algorithm. The new design approach avoids the solution of the numerically stiff parameterized ARE