含非线性扰动的退化时滞系统的滑模控制

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),f)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(...

Sliding Mode Control for Degenerate Time Lag Systems with Nonlinear Disturbances

This paper discusses sliding mode control for degenerate time lag systems.It’s different from other article that systems in this paper with both matched and mismatched nonlinear disturbances G(x(t),t) and F(x(t-τ(t)),t) which contain delay τ(t),0≤τ(t)≤h.Based on strong controllable degenerate systems equivalent transformation,the system is transformed to an equivalent form.After that,valid controller u=-M2(t)+ue drives system to the sliding surface S=-Kx1+x2=0 and maintains motion on it quickly.At last,under the condition 2‖xt1(t)TP1‖δ(x(t-τ(t)),t)≤2xT1(t)TP1x1(t-τ(t)),and via Lyapunov functions V.we obtained sufficient conditions of stabilization which LMI Ξ<0.Numerical examples demonstrate the efficiency of the result in this article.