Simultaneous state and unknown input set‐valued observers for quadratically constrained nonlinear dynamical systems

In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs states and inputs include true inputs. Necessary sufficient conditions in Linear Matrix Inequalities (LMIs) stability sense quadratic stability) proposed are derived ($\mathcal{M},\gamma$)- Quadratically Constrained (($\mathcal{M},\gamma$)-QC) systems, which includes several systems: (I) Lipschitz continuous, (II) ($\mathcal{A},\gamma$)-QC* (III) Parameter-Varying (LPV) systems. This new constraint property is at least as general incremental proven paper to embody a broad range nonlinearities. addition, design optimal $\mathcal{H}_{\infty}$ observer among those satisfy show results Uniformly Bounded-Input Bounded-State (UBIBS) estimate radii/error dynamics uniformly sequences radii. Furthermore, provide closed-form upper bound radii condition their convergence steady state. Finally, effectiveness demonstrated through illustrative examples, where compare performance our existing observers.