Introduction

In the mid-seventeenth century, Swiss mathematician Leonhard Euler proposed the “order elevation and reduction” methodology when solving higher-order nonhomogeneous ordinary differential equations, which subsequently became regarded as the canonical approach for solving such equations. Over two centuries later, Hungarian-American mathematician Rudolf Emil Kálmán pioneered the state-space model, representing systems in the temporal domain through state variables and state-space formulations, while establishing fundamental theories of controllability and observability. This established the state-space model as one of the predominant paradigms for system representation. While this modeling framework proves advantageous for state response analysis, filtering, and observer design, it exhibits inherent limitations in control input computation and, more significantly, compromises the system’s intrinsic fully-actuated properties.