On Improving the Convergence Rate of Linear Continuous-Time Systems Under Constrained Control With State Observers

A controller design methodology for linear continuous-time systems using a state observer is proposed. In particular, the objective is to smooth the discontinuity resulting from a piecewise linear control law previously proposed, which improves the convergence rate of systems under asymmetrically constrained control. The proposed method is based on the use of a non quadratic asymmetrical Lyapunov function. Both full-order observers and minimal order observers are considered to reconstruct the inaccessible state. The speed of convergence of the controlled system and the observer is improved, with smooth control vector components, that respect always the imposed asymmetric constraints.