Observers with Multiple Sliding Modes for Uncertain Linear MIMO Systems

In this paper, sliding mode observers for uncertain MIMO linear systems are developed in both the continuous and discrete-time domains. The uncertainties are characterized as unknown inputs to the system. We propose a sliding mode observer with multiple sliding modes to completely eliminate the disturbances in the sliding mode. It is shown that in the sliding mode, the system is completely stable and the estimated states converge to the actual states asymptotically. The gain design is based on standard Lyapunov analysis. Existence of the discrete-time sliding mode is proved and the gain design is based on the boundary layer thickness for the case of discrete-time systems. Numerical results demonstrate the effectiveness of the proposed method