A new H_∞ control method of impulsive dynamical linear systems: H_∞ control criterion constrained by convergence rate

Abstract

In this article, a new H∞$$ {H}_{\infty } $$ control criterion of impulsive dynamic linear systems is proposed, that is, H∞$$ {H}_{\infty } $$ control criterion based on convergence rate. The conclusion can not only satisfy the target system H∞$$ {H}_{\infty } $$ control criterion, but also reveal the dynamic performance index, such as the convergence rate of its state, which can achieve the purpose of accurate control and have certain anti‐interference ability. According to the relationship between the eigenvalues (poles) and performances of systems, the conditions of interval stability and interval stabilization are obtained via the idea of generalized pole placement and equivalent systems. Then, combined with the classical H∞$$ {H}_{\infty } $$ control criterion, H∞$$ {H}_{\infty } $$ control criterion constrained by convergence rate is investigated. Referring to the 𝒞 programming language, system eigenvalues adjustment algorithm is designed. Through the cooperation between the algorithm and the above criteria, the target system has certain anti‐interference ability and its state convergence speed is precisely controlled. Finally, the advantages mentioned above are illustrated by two examples.