Robust Multivariable Sliding Mode Control Design for Minimum Estimated Reaching Time–Fully and Over‐Actuated Systems

ABSTRACT

This paper addresses two minimum reaching time control problems for a class of fully actuated multivariable systems with an uncertain input matrix by adopting two different classes of Lyapunov functions. The well‐known relay Variable Structure Control and Unit Vector Control strategies are analyzed, with the primary objective of designing optimal and robust state feedback gains that ensure minimum finite‐time convergence to the origin. This is achieved in the presence of convex bounded parameter uncertainty and norm‐bounded exogenous disturbances. In both cases, the optimality conditions are expressed through Linear Matrix Inequalities, which are solved efficiently within the framework of multivariable systems using existing numerical tools. The theoretical results are applied to two practically motivated examples.