A survey on High-Order Sliding-Mode control design using Lyapunov functions

Abstract

A survey of (some) recent Lyapunov-based methods to analyze and design High-Order Sliding-Mode (HOSM) controllers and observers is presented. This overview includes also some novel algorithms, taking advantage of a discontinuous integral action, to attain a High-Order Sliding-Mode using a continuous control signal. This account starts presenting the design based on Lyapunov functions of classical sliding-mode controllers using a discontinuous state feedback control law to impose a high-order sliding-mode of arbitrary order. In order to estimate in finite-time the required derivatives of the measured signals for the implementation of the controllers, a Lyapunov-based design of the well-known robust and exact differentiator is shown. As a mechanism to reduce the effect of the undesirable chattering effect a recent method for higher-order sliding-mode controllers has been developed, using a continuous state feedback in conjunction with a discontinuous integral action to enforce a sliding-mode by means of a continuous control signal. The analysis and design tool for this integral controller is also an explicit, strict and particularly tailored Lyapunov function. In order to make this recount accessible to a wide audience the presentation is restricted to the main results, without giving proofs or design details, and leaving aside the rigorous mathematical machinery. For this the main references are provided.