Finite-Time Annular Domain <i>H</i> ₂ / <i>H</i> _∞ Filtering for Stochastic Markovian Jump Systems and Its Applications in PWM Circuits

This brief addresses the finite-time annular domain (FTAD) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}/H_{\infty }$ </tex-math></inline-formula> filtering problem for linear stochastic Markovian jump systems (SMJSs) subject to Brownian motion and Poisson noise. By adopting the mode-dependent parameter approach and leveraging the reverse differential Gronwall inequality and the Itô-Levy formula, novel sufficient conditions ensuring the existence of such <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}/H_{\infty }$ </tex-math></inline-formula> filter are established. This condition is much less conservative, thus greatly extending the scope of solutions. Additionally, an algorithm is designed to determine the parameter ranges and show the relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance metrics. Finally, a PWM-driven circuit is used to demonstrate the practicality of the proposed approach.