Stability of Markov jump systems with quadratic terms and its application to RLC circuits

Abstract

The paper presents results for the second moment stability of continuous-time Markov jump systems with quadratic terms, aiming for engineering applications. Quadratic terms stem from physical constraints in applications, as in electronic circuits based on resistor (R), inductor (L), and capacitor (C). In the paper, an RLC circuit supplied a load driven by jumps produced by a Markov chain—the RLC circuit used sensors that measured the quadratic of electrical currents and voltages. Our result was then used to design a stabilizing controller for the RLC circuit with measurements based on that quadratic terms. The experimental data confirm the usefulness of our approach.