Parametric approaches to sliding mode design for inear multivariable systems

Abstract

The parametric approaches to sliding mode design are newly proposed for the class of multivariable systems. Our approach is based on an explicit formula for representing all the sliding modes using the Lyapunov matrices of full order. By manipulating Lyapunov matrices, the sliding modes which satisfy the design criteria such as the quadratic performance optimization and robust stability to parametric uncertainty, etc., can be easily obtained. The proposed approach enables us to adopt a variety of Lyapunov- (or Riccati-) based approaches to the sliding mode design. Applications to the quadratic performance optimization problem, uncertain systems, systems with uncertain state delay, and the pole-clustering problem are discussed.