Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Abstract

We address the design of dynamic parameter-dependent controllers with antiwindup action to locally stabilize in the input-to-state sense a class of discrete-time linear parameter-varying (LPV) systems. Such a class consists of systems with delayed state, saturating actuators, and subject to energy bounded disturbances. Moreover, the interval time-varying delay can have a limited variation rate between two consecutive instants allowing to achieve less conservative design conditions. Differently from other conditions in the literature, the proposed convex synthesis methods allow to design dynamic controllers of different orders. Additionally, the user can choose to feed back only the current output of the system or its delayed ones. Thanks to the embedded (parameter dependent) antiwindup action, it is possible, for instance, to enlarge the region of admissible initial conditions or the maximum admissible disturbance energy. To illustrate the efficiency of our approach, we present numerical examples to compare with other methods from the literature. K E Y W O R D S 2-disturbances, dynamic controller, local input-to-state stability, LPV discrete-time systems, saturating actuators, time-varying delay with bounded variation rate Abbreviations: LMI, linear matrix inequality; LPV, linear parameter-varying.

Local input‐to‐state stability analysis on compact set for disturbance observer‐based uncertain multivariable nonlinear control systems

“…A LISS control design has also been proposed for systems with time‐delay 8,9 . However, the above‐mentioned studies did not consider the state‐dependent nonlinearity and uncertainties, which limits their application.…”