Considering that many processes and systems in real world applications can be modeled as switched systems, observers synthesis for this class of systems has received a growing interest in the last decades. This thesis intends to provide some contributions to the state-of-the-art in the field of robust state estimation for Switched Dynamical Systems subject to unknown parameters, external disturbances and/or measurement noise. One of the main feature of this dissertation regarding the available literature is that, no statistical evaluation of uncertainties is needed, only the knowledge of the interval boundaries to which these latter belong is required. The proposed methodologies are based on the so-called set-based approaches which provide an estimate of the set of admissible values of the state vector at each time-instant. The present thesis contributes and solves the problem of robust state bounding estimation using two paradigms which are: i) Interval Observer techniques based on cooperative system theory: where new interval observer structures are introduced and shown to have certain advantages over the classical interval observers when studying robustness and cooperativity issues. Sufficient conditions for proving the stability and cooperativity of the interval observer estimation error are provided in terms of Linear Matrix Inequalities (LMIs) constraints obtained using a combination of Lyapunov theory and Input-to-State Stability concept. In order to enhance the estimation accuracy and robustness, an explicit bound of the interval error is guaranteed and optimized for better estimation precision. ii) Set-membership observer techniques based on set theory: where switched observers based on interval characterization of the estimation error are proposed first. Next, new zonotopic state estimation approach based on minimizing the radius of the zonotope is developed. In this spirit, new method leading to the resolution of an optimization problem in the form of LMIs has been proposed. The above-mentioned contributions have been applied to state estimation and Fault Detection in Vehicle Lateral Dynamics. Application to real data recorded with a prototype equipped vehicle demonstrates the relevance and efficiency of the proposed approaches.