Nonlinear control of linear multivariable systems via state-dependent feedback gains

It is often desirable to have controllers which respond fast to large errors and which respond slowly to the small errors that are often due to sensor noise. Some nonlinear controllers having these properties are developed here by modifying optimal linear state feedback controllers so that they have state-dependent gains. A general approach is developed for the nonlinear control of multivariable systems such that the transient responses exhibit the desired properties, and the closed-loop systems are asymptotically stable.