A Study on Observer Design for a Class of Nonlinear Systems using Lyapunov Stability

Abstract This research proposes a novel Lyapunov-based method for designing an observer for a class of nonlinear systems whose unmeasured states appear linearly in the state-space model, while the coefficients can be nonlinear functions of the measured states and time. In the other words equations can be express as a Linear Parameter-Varying (LPV) systems in which the parameter-dependent matrices depend on time and accessible variables. Many papers that deal with developing an observer for LPV systems assume that the variable parts are bounded for the feasibility of the design. By extending the conventional method which is used to estimate the state variables in linear systems, this study introduces an innovative scheme that has no limitations on the scheduling parameters. In the error equations, which quantify the discrepancy between the actual system and the estimated system, the matrices dependent on scheduling parameters can exhibit stable eigenvalues, provided that the observer gain matrix is selected appropriately. This matrix should be a continuous function. The stability of the eigenvalues implies that the observer can accurately estimate the state variables, as shown by using Lyapunov stability analysis. Mathematics Subject Classification 34D20 58E25