Modeling, Simulation, and Robust Control of An Inverted Pendulum System using LQR, $H_{2}$ and $H_{\infty}$ Controllers

The inverted pendulum represents a classic nonlinear, underactuated, and inherently unstable system susceptible to external disturbances. This paper presents a comparative study of advanced control strategies - namely, Linear Quadratic Regulator (LQR), <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{H}_{2}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{H}_{\infty}$</tex> controllers for stabilization of a Nonlinear Parameter-Varying (NLPV) inverted pendulum system. The study includes physical system development, parameter identification, controller design, and performance evaluation through simulations and real-time experiments.