In this research, we suggest a new fuzzy adaptive state-feedback control strategy for unknown nonlinear multivariable systems for which the input-gains matrix is not necessarily symmetric and is characterized by non-zero leading principle minors. A linearly parameterized fuzzy system is used to appropriately model the uncertainties. When designing our control scheme and studying the stability analysis, a decomposition property of the input-gain matrix is employed. A proportional-integral (PI) adaptation law is suggested to enhance the adaptive parameter convergence. An appropriate Lyapunov function is exploited to study the stability of the corresponding closed-loop control system as well as to derive the adaptation laws. Numerical simulations and a detailed comparison study are given to evaluate the efficiency of our suggested control methodology.