In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.Keywords: nonlinear uncertain dynamical systems; multi-input/multi-output systems; robust control; Lyapunov methods
Nomenclature x(t) System states x (i) (t) ith-order time derivative of x(t) H(·), h(·) Functional containing uncertain components G(·), g(·)Real-valued matrix with nonzero leading principal minors τ (t), τ 1 (t), τ 2 (t) Control inputs X(t) Combined state vector S(X) Symmetric positive definite matrix D Diagonal matrix with entries ±1 U(X) Unity upper triangular matriẋ τ (t) Time derivative of control input ϕ (X, x (n) ) Auxiliary function m Positive bounding constant m (X) Positive non-decreasing bounding function x r (t) Reference trajectory e 1 (t) Output tracking error e i (t) Auxiliary error signals for i = 2, . . ., n r(t) Filtered error signal a i, j Positive-valued coefficients generated via a Fibonacci number series I m m × m identity matrix 0 m × 1