Observers for systems with nonlinearities satisfying incremental quadratic constraints

Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

“…Note that the term D q is included to treat systems where the nonlinear term depends on the derivative of a state variable. Characterization of the nonlinear element φ(s, q) is based on a set of symmetric matrices M, which is referred to as incremental multiplier matrices (Açikmese and Corless, 2011). Specifically, for all M ∈ M the following incremental quadratic constraint holds:…”

“…Moodi and M. Farrokhi However, unlike in the previous works, this nonlinear term is not assumed to be Lipschitz, which is a mild condition but results in conservative designs. Instead, in this paper, the incremental Quadratic Constraint (δQC) is adopted (Açikmese and Corless, 2011). This constraint is less conservative compared with the Lipschitz condition.…”

Decentralized observers with consensus filters for distributed discrete-time linear systems

“…LMI based centralized observer design is considered for a general class of continuous-time systems with nonlinear and time-varying terms satisfying incremental quadratic inequalities (Açıkmeşe & Corless, 2011). LMI based decentralized estimators are considered in Subbotin and Smith (2009) for fixed and stochastic communication networks.…”

Observers for interconnected nonlinear and linear systems

“…constraints (Açıkmeşe and Corless, 2011); sliding observers (Slotine, Hedrick, and Misawa, 1987;Drakunov, 1992); and moving-horizon estimation (Moraal and Grizzle, 1995). This list is by no means exhaustive, and in addition to general methodologies, application-specific designs proliferate throughout the literature.…”

“…Specifically, many continuoustime designs enable the construction of a Lyapunov function V (t,x) with the properties that α 1 x 2 ≤ V (t,x) ≤ α 2 x 2 , V (t,x) ≤ −α 3 x 2 , and [∂V /∂x](t,x) ≤ α 4 x , wherex is the observation error variable (e.g., Krener and Isidori, 1983;Marino and Tomei, 1995;Rajamani, 1998;Zemouche et al, 2008;Phanomchoeng and Rajamani, 2010;Esfandiari and Khalil, 1987;Saberi and Sannuti, 1990;Gauthier et al, 1992;Bornard and Hammouri, 2002;Grip and Saberi, 2010;Arcak and Kokotović, 2001;Fan and Arcak, 2003;Açıkmeşe and Corless, 2011). This is not surprising, given that many designs are based at least in part on linear theory, which yields quadratic-type Lyapunov functions.…”