In this paper, a cost-guaranteed fractional PID control strategy is proposed for fractional order uncertain systems (FOUSs) with time-varying delay regarding finite-time boundedness (FTB) analysis, where the fractional order lies within (0,1). Fractional order PID control is typically studied in the frequency domain, but for an uncertain system with time-varying delay, it is more convenient to conduct the study in the time domain. A novel Lyapunov–Krasovskii function is constructed. Based on this and a fractional order integral matrix inequality, several corresponding less conservative sufficient conditions are derived to guarantee the FTB of the system. By employing LQR and LMI approaches, the proposed conditions can be solved using some standard numerical packages. Through fine-tuning the conditions, the derived results can also be effectively applied to asymptotic stability analysis. Two numerical examples are presented, which further validate the introduced theoretical formulation and highlight its effectiveness through result comparisons.
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