Interval Estimation for Uncertain Discrete-Time Switched Linear Systems Using $H_{\infty}$ Observer and Zonotopic Techniques

This work proposes an interval state estimation method for discrete-time switched linear systems (SLS) systems subject to bounded uncertainties. our task demands us to calculate a zonotopic outer estimation of the state. The first step is to develop a switched <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex>-based observer that reduces the effects of uncertainties and provides a point estimate of the state vector. Following that, interval estimation is accomplished by integrating robust point state estimation with zonotopic analysis. By adopting a common quadratic Lyapunov function, the observer gains matrices are determined by solving Linear Matrix Inequalities (LMIs). The effectiveness and the feasibility of the proposed design is highlighted using a numerical example.