Two-sided linear matrix inequality solution of affine input matrix for feasible discrete finite-time sliding mode control of uncertain nonlinear mechanical machines

Abstract

In this article, a new control method is proposed based on finite-time discrete sliding mode control for uncertain multi-input multi-output systems which are affine to their inputs considering uncertain input multipliers in the case where signs of input gains remain constant over uncertainty spaces. In addition, a method for solving a set of convex control inequalities is introduced. The proposed control strategy is based on merging data obtained from investigation of common candidate Lyapunov functions assigned to various subsystems and their subsequent decoupling based on matrix elementary row operations. Initially, separate sliding functions corresponding to a single degree of freedom are assigned to each subsystem in the overall multi-input multi-output system, which results in obtaining a convex inequality corresponding to input bounds. Stacking the data obtained from various subsystems, the product of the uncertain input gain matrix in input vector is obtained as the middle term in a set of convex inequalities. Subsequently, the convex inequality is solved according to a set of matrix elementary row operations transforming the corresponding input matrix to row echelon form such that the bounds of each input are clearly expressed. Then, based on assigning input bounds proximity factors to each lower bound–upper bound duo, appropriate control inputs are generated. Chattering effects are eliminated as no switching term is included in construction of the control model. Effectiveness of the proposed method is demonstrated using numerical simulations. The implementation of control algorithm using microprocessors is also illustrated, indicating the feasibility of digital application.