2022/04/02 by Mohamed A. Mabrok, Mabrok, Mohamed
Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Piezoelectric Actuators and Control
paper · pdf · doi:10.48550/arxiv.2204.00952
openalex publication_date 2022/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The negative imaginary (NI) systems theory has attracted interests due to the robustness properties of feedback interconnected NI systems. However, a full output optimal controller-synthesis methodology, for such class of systems, is yet to exist. In order to develop a solution towards this problem, we first develop a methodology to find the nearest NI system to a non NI system. This later problem stated as follows: for any linear time invariant (LTI) system defined by the state space matrices (A, B, C, D), find the nearest NI system, with the state space matrices (A+ΔA,B+ΔB,C+ΔC,D+ΔD), such that the norm of (ΔA,ΔB,ΔC,ΔD) is minimized. Then, this methodology will be used to find the nearest optimal controller for a given NI plant. In other words, for a given NI system, an optimal control methodology, such as LQG, is used to design an optimal controller that satisfy a particular performance measure. Then, the developed methodology of finding the nearest NI system is used, as a near-optimal control synthesis methodology, to find the nearest NI system to the designed optimal controller. Hence, the synthesized controller satisfy the NI property and therefore guarantee a robust feedback loop with the negative imaginary system under control.