$$H_{\infty }$$ Optimization-Based Stabilization for Nonlinear Disturbed Time Delay Systems

Abstract

This paper contemplates designing a $$H_{\infty }$$ dynamic output-feedback decentralized control for nonlinear interconnected disturbed time delay systems. Pursuant to Lyapunov–Krasovskii functional techniques and linear matrix inequality methods, asymptotic stability conditions for the robust stability and stabilization of the studied system are conducted in an optimization problem subject to linear matrix inequalities. The resolution of such a problem enables computing jointly the robust observation and control gain matrices, maximizing the bounds of nonlinear interconnections tolerated by the system without being unstable, improving the performance of the proposed control strategy by minimizing a $$H_{\infty }$$ criterion and ensuring the stability of the closed-loop system despite exogenous disturbances applied to the subsystems. Simulation results are provided by a prominent application example of a 3-interconnected machine power system with time delay to demonstrate the efficacy of the designed delay-independent control approach.