Lyapunov equation

Lyapunov equation

Numerical and Computational Issues in Linear Control and System Theory

Published in William S. Levine, Control System Fundamentals, 2019

A.J. Laub, R.V. Patel, P.M. Van Dooren

Certain matrix equations arise naturally in linear control and system theory. Among those frequently encountered in the analysis and design of continuous-time systems are the Lyapunov equation () AX+XAT+Q=0,

Continuous dynamic gain scheduling control for input-saturated switched systems

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Journal Information

Published in International Journal of Systems Science, 2022

Qian Wang, Qingxia Lin, Yuetao Yang

In this paper, we study the continuous dynamic gain scheduling control for the input-saturated switched system by the designed time-varying parameter. The time-varying parameter can be obtained by solving a differential equation. The state feedback controller is designed based on the parametric Lyapunov equation. And a compensator-based output feedback controller was designed for the input-saturated switched system with parametric uncertainties and external disturbance based on the sliding mode control and gain scheduling control. The exponential stability analysis was given and the closed-loop system has better dynamic performance under the designed controllers. The proposed control method only needs to solve the parametric Lyapunov equation online, and the computation is relatively small. The simulation results showed the effectiveness of the designed controllers. In the future work, we will extend the proposed methods to the nonlinear system (Mobayen & Tchier, 2017; Zong et al., 2021) and the distributionally robust optimisation control (Li et al., 2018).

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Numerical and Computational Issues in Linear Control and System Theory

Continuous dynamic gain scheduling control for input-saturated switched systems