In this chapter, the problem of continuous and discrete state estimation for switched nonlinear systems is solved using High-Order Sliding-Mode techniques. In the first part of this chapter, the systems with exogenous switchings are studied. The solvability of the observation problem, for the continuous and discrete states, is proposed using structural properties of the system. This structural properties are exploited to design the observers. The high-order sliding-mode techniques are introduced to guarantee finite time convergence to zero of the estimation error for the continuous state. The discrete state is reconstructed using the information of the equivalent output injection. The continuous state observation, discrete state and unknown input reconstruction for switched systems with autonomous switchings are realized in the second part of the chapter. In this part, the structural properties of the systems are exploited to ensure the observability of the continuous and discrete states. Finite-time convergence to zero of the estimation error, for continuous and discrete states, are achieved. The information of the equivalent output injection is used for unknown input reconstruction. Simulation results are provided to illustrate the methods exposed in the chapter.
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