On sliding mode observers via equivalent control approach

In this paper, sliding mode observer design principles based on the equivalent control approach are discussed for a linear time invariant system both in continuous and discrete time. For the continuous case, the observer is designed using a recursive procedure; however, the observer is eventually expressed as a replica of the original system with an additional auxiliary input with a certain nested structure. A direct discrete time counterpart of the sliding mode realization of a reduced order asymptotic observer using the discrete time equivalent control is also developed. Simulation of a linearized truck-trailer during a manoeuvre illustrates the approach. Results show the effectiveness and the finite time convergence characteristics of the proposed discrete and continuous time sliding mode observers.