Zonotopic State Estimation for Uncertain Switched Positive Systems

This paper investigates the zonotopic interval estimation problem of uncertain switched positive systems. Firstly, we demonstrate the positivity of the observer and the uncertain error system. Subsequently, we establish several linear programming conditions to ensure the stability and $\ell_{\infty}$ performance for the underlying system by constructing a suitable copositive multiple Lyapunov function. Then, a joint design scheme is proposed for the switching signal and mode-dependent positive linear observer is proposed. Furthermore, we establish the zonotopic interval estimation of uncertain switched positive systems, computing the estimation bounds for the system states. Finally, the advantages and effectiveness of the proposed state estimation approach are verified through a simulation example.