Sum-of-squares based observer design for polynomial systems with a known fixed time delay

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

“…Using (Lemma 4.2, p. 861 in [14]), from (26), it follows that η(e, x) Π e G(x, L) + Π x g(x) w ≤ η(e, x) η(e, x) + µ 2 2 w w . and, after replacing this upper bound in Equation (28), it follows that (18) (see the proof of Theorem 1) holds if (25) is satisfied, which allows for concluding.…”

“…for all t ≥ t 0 ≥ 0, which provides an upper bound on V(e(t), x(t)) based on the initial conditions and a measure of the "energy" of the noises. If V is a continuously differentiable function, (14) holds if (13) is satisfied. The function V is thus a storage function, while α 3 and α 4 have to be regarded as dissipation and supply rates, respectively.…”

“…Moreover, the condition (31) is easier to be satisfied as compared with (30). Indeed, additional constraints can be introduced by constraining the estimation error to belong to suitable compact sets and/or taking into account the boundedness of the state trajectories [14]. This allows for facilitating feasibility when solving Problem 2.…”

“…ISS sampled-data observers are analyzed in [12]. The design of ISS estimators is addressed in [13][14][15][16].…”

Robust sampled-data observer design for Lipschitz nonlinear systems

“…Sufficient conditions in terms of LMIs are proposed to ensure the convergence of the observer errors. An observer is also proposed for time-delayed systems with polynomial nonlinearities [20]. However, some of the proposed approaches suffer some problems such as too many assumptions and constraints.…”