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Time delay correlation H-infinity control method for linear singular system with uncertain time delay

A singular system and control method technology, applied in the field of time-delay dependent H∞ control

Active Publication Date: 2020-05-15
HARBIN ENG UNIV
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Problems solved by technology

The stability judgment conditions given by the first category do not contain time-delay information, and have nothing to do with the size of the time-delay. For small-delay systems, this type of condition is very conservative

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  • Time delay correlation H-infinity control method for linear singular system with uncertain time delay
  • Time delay correlation H-infinity control method for linear singular system with uncertain time delay
  • Time delay correlation H-infinity control method for linear singular system with uncertain time delay

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Embodiment Construction

[0058] The specific embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0059] The present invention divides the system state into two parts: the slow subsystem state x 1 and fast subsystem state x 2 , give the state space description of the linear time-delay singular system; select the Lyapunov-Krasovskii function, use the method of combining the improved free weight and the Lyapunov-Krasovskii function, derive and prove that the system is internally stable, and has a given H∞ disturbance suppression Bounded Real Lemma and LMI Inequality of Level γ; Design of Memoryless Controller u(t)=Kx Based on Slow Substate Feedback 1 (t), so that the closed-loop system is stable, and has a given disturbance suppression level γ under the zero initial condition, deduces the relevant theorems and gives the stability conditions of the system; performs contract transformation on the matrix inequality in the theorem, for The n...

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Abstract

The invention aims to provide a time delay correlation H-infinity control method for a linear singular system with uncertain time delay. The method comprises the following steps: giving a state spacedescription of the linear singular system with the uncertain time delay; selecting a Lyapunov-Krasovskii function, and deriving and proving a bounded real lemma and an LMI inequality which enable thesystem to be stable and have a given H-infinity disturbance suppression level gamma by utilizing a method of combining an improved free weight and the Lyapunov-Krasovskii function; designing a non-memory controller u(t) = Kx1 (t) based on slow sub-state feedback, and giving a matrix inequality condition which enables a closed-loop system to be stable and contains nonlinearity; performing contracttransformation on the matrix inequality condition; defining new extra matrix variables and matrix inverse limiting conditions for nonlinear terms in a matrix inequality, and using a cone compensationlinearization iteration method to convert a solving problem of the nonlinear matrix inequality into a nonlinear minimization problem, so that an obtained result has a given disturbance suppression level gamma while ensuring the stability of a closed-loop system.

Description

technical field [0001] The invention belongs to the technical field of linear time-delay system stability and robust control, in particular to a time-delay dependent H∞ control method for a linear singular system with uncertain time-delay. Background technique [0002] For linear time-delay systems, whether they are general systems or singular systems, the premise of control and design is to ensure the stability of the system. There are mainly two methods to study the stability of time-delay systems, the frequency domain method and the time domain method. Among them, the frequency domain method judges the stability according to the roots of the characteristic equation (for time-delay systems, the characteristic equation is a transcendental equation), so when the order of the system is relatively high, the judgment of its stability, that is, the distribution of the roots, will be It is more complicated, so the frequency domain method is used less. The time-domain method is ...

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Application Information

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IPC IPC(8): G05B13/04
CPCG05B13/042
Inventor 刘彦文张书浩刘寅林綦志刚李松峰
Owner HARBIN ENG UNIV
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