The ℓ∞/p$$ {\ell}_{\infty /p} $$‐gains for discrete‐time observer‐based event‐triggered systems

This paper aims at computing two types of system gains for discrete‐time observer‐based event‐triggered systems (ETSs) via the linear matrix inequality (LMI) approach. More precisely, an event‐trigger mechanism (ETM) is considered for the discrete‐time control systems consisting of a static controller and a Luenberger observer to determine whether or not the input signal for the controller is updated to the estimated value from the observer. For a tractable treatment of the input/output behavior of such ETMs, we derive their closed‐form representation through a piecewise linear difference equation. Based on this representation, we establish LMI‐based computation approaches to the gains for the ETSs from ℓp$$ {\ell}_p $$ to ℓ∞$$ {\ell}_{\infty } $$ (denoted by ℓ∞/p$$ {\ell}_{\infty /p} $$) with p=2,∞$$ p=2,\infty $$. Finally, the effectiveness of the overall arguments is verified through a numerical example.