This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e f...This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e form with negative semi--definite derivative (i.e. V≤0).展开更多
Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, pro...Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, provided that the exceptional set E has σ-finite H^1-measure.Moreover, f has finite distortion, differentiable a.e. and the Jacobian Jf 〉 0 a.e.展开更多
文摘This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e form with negative semi--definite derivative (i.e. V≤0).
基金Supported partially by the Academy of Finland(Grant No.131477)the Magnus Ehrnrooth foundation
文摘Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, provided that the exceptional set E has σ-finite H^1-measure.Moreover, f has finite distortion, differentiable a.e. and the Jacobian Jf 〉 0 a.e.
