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文章主要讨论了含有非线性扰动的退化时滞系统的滑模控制问题。与已有文献不同之处在于系统中同时含有匹配的和不匹配的不确定项G(x(t),t)以及F(x(t-τ(t)),t),且不匹配项中存在时滞τ(t),其中0≤τ(t)≤h。文章首先基于强能控退化系统的等价变换,将系统化为一等价系统。之后,再利用有效的控制器u=-Mx2(t)+ue的设计,使得系统能快速到达滑模面S=-Kx1+x2=0上并保持在滑模面上运动。最后,在条件:2‖xT1(t)TP1‖δ(x(t-τ(t)),t)≤2xT1(t)TP1x1(t-τ(t))之下,利用Lyapunov泛函V的构造得出此类系统渐近稳定的充分条件—线性矩阵不等式Ξ<0。文中的数值例子说明了结论的有效性。
The paper mainly discusses the sliding mode control problem of degenerate time-delay systems with nonlinear disturbances. It differs from the existing literature in that the system contains both the unmatched and unmatched uncertainties G (x (t), t) and F (x (t-τ (t)), t) There is a time lag τ (t), where 0 ≦ τ (t) ≦ h. Firstly, based on the equivalence transformation of the strong controllable degeneration system, the article will be systematized into an equivalent system. Then, the design of the effective controller u = -Mx2 (t) + ue is used to make the system quickly reach the sliding surface S = -Kx1 + x2 = 0 and keep moving on the sliding surface. Finally, using the Lyapunov functional V (t-τ (t)) under the condition: 2 || The sufficient conditions for the asymptotic stability of such a system are obtained. The linear matrix inequality Ξ <0. The numerical examples in this paper illustrate the validity of the conclusion.