An h∞ control method for a class of discrete systems with time-delayed linear parameter variations

Abstract

The invention discloses an H-infinity control method for a time-delay linear parameter variation discrete system. The condition that a linear parameter variation control system has bounded nonlinearity, time delay, time variation of model parameters and variable controller gain is considered, and the method comprises the steps that firstly, a closed-loop time-delay linear parameter variation discrete control system model is established, then a proper Lyapunov function is structured, sufficient conditions for stability of the system and existence of an H-infinity controller are obtained based on the Lyapunov stability theory and a linear matrix inequality analysis method, and meanwhile the solving problem of an infinite dimensional linear matrix inequality set is approximated into the solving problem of a finite dimensional linear matrix inequality set with an approximate base function and the grid technology; finally, a Matlab LMI tool kit is used for solving, and it is given that the H-infinity controller gain matrix of the time-delay linear parameter variation discrete system is K=R(rho)V<-1>. According to the H-infinity control method for the time-delay linear parameter variation discrete system, the situations of time delay and stochastic disturbance are considered, higher practical meaning is achieved, the method is suitable for common H-infinity control, and the conservative property of H-infinity controller design is reduced.

Description

technical field [0001] The present invention relates to time-delay linear parameter variation discrete-time control systems and H ∞ control, especially involving a class of linear parameter varying discrete-time control systems with state delays ∞ Control Method. Background technique [0002] Linear Parameter-Varying Systems (LPV) are an important class of time-varying systems, whose state-space matrix is ​​a deterministic function of time-varying parameters that can be measured in real time and vary on a closed set. Because it can describe the nonlinear and time-varying characteristics of a class of actual dynamic systems, the linear parameter changing system has become a hot spot in the field of control theory in recent years, and its theory has been successfully applied in aviation, aerospace, robotics and industrial processes. areas of control. At the same time, due to the large inertia link, the signal transmission process and the complex online analyzer, etc. will i...

AI Technical Summary

Problems solved by technology

The existence of time lag makes the analysis and synthesis of the system more complicated and difficult, and the existence of time lag is often one of the root causes of system instability and system performance deterioration

The controller or filter designed by ignoring the inherent time delay phenomenon in the system will be unstable or degrade in actual application

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