Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty

In this paper, a robust stabilization problem for a class of uncertain systems is studied using sliding mode techniques. Matched and mismatched uncertainties are both considered. By employing the sliding surface proposed by Edwards and Spurgeon in [Int J Control 1995; 62(5): 1129–1144], the stability of the sliding mode is shown first. Then, an asymptotic observer is established to estimate the system state variable based on a constrained Lyapunov equation, and a variable structure controller is proposed to stabilize the system by exploiting the estimated state and system output. The two major limitations in [IEEE Trans Autom Control 1996; 41(11): 1691–1693] are eliminated. Finally, a simulation study based on a simplified model of the HIRM aircraft system is used to illustrate the effectiveness of the results.