Observer design for a class of discrete-time quasi-LPV systems with unknown parameters: Algebraic approach

This paper presents a new observer design approach for a class of discrete-time nonlinear systems described by a polytopic quasi-LPV (qLPV) models. The contribution consists in developing an observer for qLPV systems where the parameters depend on the unmeasured states of the system. The approach consists in combining the algebraic techniques with polytopic qLPV observers. Firstly, with the assumption that the nonlinear system is algebraic, or partially algebraic, observable, the unmeasured states involved in the parameters are estimated, exactly, in finite time which provides an exact estimation of the parameters. Secondly, the qLPV observer is designed by using the estimated parameters and the its finite time estimation property. Asymptotic convergence of the state estimation error is then obtained by Lyapunov analysis and LMI constraints are established, ensuring such a property and provide a way to design the gains of the observer. In addition, the transient phase is analyzed and an optimization problem under LMI constraints is provided to minimize the over-shoot of the state estimation error in the transient phase. An example is provided to illustrate the performances of the proposed approach and comparisons.