Application of Mathematics for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Interval Plant

ABSTRACT In this article, we present a robust control problem wherein represents a family of interval plants. For this particular problem, we introduce four Kharitonov polynomials uniquely by minimizing and maximizing the concept of multilinear functions with uncertain parameters and for the plant and where denotes the conjugate of and , with representing frequency within a specified domain. This technique yields a Kharitonov rectangle or box whose every four vertices are represented by four unique Kharitonov polynomials , each is denoted by and and this rectangle characterizes both robust stability and robustly strictly positive real (SPR) for the family of interval plants (). Thus, the introduction of this Kharitonov rectangle stands as a novel innovation in this article. Our contribution encompasses two key aspects. Initially, we demonstrate the stability of the four unique Kharitonov polynomials employing Hurwitz stability criteria, followed by the utilization of Kharitonov's theorem to ensure robust stability of . Subsequently, to establish robustly SPR of , we analyze the SPR of each interval plant concerning the stability of and , adhering to the condition . Additionally, we provide a detailed illustrative example. Furthermore, we demonstrate the motion of the Kharitonov rectangle and the robust stability test through simulation.