Robust switching control design for matrix second order systems: Application to robotic cane platform

Abstract

This paper addresses the switching control design problem for a class of nonlinear matrix second-order systems that characterize the dynamics of robotic and multibody systems. These systems are inherently characterized by significant nonlinearities and are subject to uncertainties, parameter variations, and external disturbances, which pose substantial challenges for control design. Analytical solutions for such control problems are often intractable, necessitating the use of numerical optimization techniques. This study presents sufficient conditions, derived from Lyapunov stability theory, for synthesizing switching feedback controllers that ensure system stability with guaranteed $H_{\infty }$ performance. The approach leverages the Linear Parameter Varying (LPV) representation of the nonlinear dynamics through Takagi–Sugeno (T-S) modeling methodology. The proposed stability conditions are formulated as Linear Matrix Inequalities (LMIs), enabling efficient computation using standard convex optimization software. Comprehensive simulation studies demonstrate that the proposed switching control strategy, applicable to a broad class of nonlinear matrix second-order systems, significantly outperforms conventional weighted gain-scheduling approaches in terms of feasibility regions and $H_{\infty }$ performance indices. Experimental validation on a robotic cane platform confirms the practical effectiveness of the proposed methodology, achieving nice dynamic performance and robust disturbance rejection capabilities.