Low - and - High Gain Design Technique for Linear SystemsSubject to Input Saturation

The low-and-high gain design technique, which was initiated in 10] for a chain of integrators and completed in 13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semi-global 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 in 10] is based on explicit eigenstructure assignment, its full development in 13] 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 explicit eigenstructure assignment. The new design approach avoids the solution of the numerically stii parameterized ARE.