Practical stabilizability via a relaxed mismatched criterion

The authors consider a linear dynamic system model whose description includes time-varying parametric uncertainties in the system state matrix as well as disturbance inputs and noisy measurements. The disturbance and measurement noise are assumed to be zero, and a relaxed mismatch criterion is shown to be a sufficient condition for guaranteeing linear quadratic stabilizability. The original system with nonzero disturbance and measurement noise is then shown to be practically stabilizable using a nonlinear control. That is, upon reintroducing disturbance input and assuming measured state feedback, the quadratic Lyapunov function generated in the first step forms the basis of an additional nonlinear saturating control component that can be used to achieve a minimum for the ultimate bound on the state