pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation

Highlights：

• Retarded discrete state delay and distributed delay are considered for IMJSs simultaneously;

• Besides S-F decomposition and singular value decomposition techniques, Barbalat’s lemma is employed to prove asymptotic admissibility of delayed IMJSs when τ(t)=τ. Then the delayed IMJSs not only satisfy stochastic stability, but also satisfy almost sure asymptotic stability;

• The difficulties of controller design via S-F decomposition and singular value decomposition are overcome by matrix transformation technique in terms of LMIs;

• Limitations of implicit systems normalization via P-D feedback control are uncovered and addressed by virtue of the proportional state feedback controller design method, which does not need the rigorous condition of rank(E,B)=n.