Geometric stabilization of discrete‐time systems via dissipativity approach and output feedback control

Abstract

Geometric stabilizability is studied for nonlinear discrete‐time systems (DTS) utilizing linear static output feedback (SOF). Initially, a linear SOF controller is designed such that nonlinear DTS achieve geometric stabilizability. Utilizing the concept of geometric QSR‐dissipativity (GQSR‐D), a condition both sufficient and necessary is proffered to guarantee geometric stabilizability for nonlinear DTS. Subsequently, the necessary conditions of linear matrix inequality (LMI) are delineated to ascertain the stability of a system employing linear SOF. A new sufficient and necessary condition is provided aiming to stabilize the linear time‐invariant (LTI) DTS based on GQSR‐D. Lastly, examples are furnished to elucidate the efficacy of the results, thereby reinforcing their practical applicability.