Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints

Abstract

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

Consensus Control of Nonlinear Multiagent Systems with Incremental Quadratic Constraints and Time Delays

“…Actually, δQC include many common nonlinearities as some special cases, such as the sector constraint, slope-restricted, Lipschitz, and one-side Lipschitz nonlinearities. We refer the interested readers to [26][27][28][29][30][31][32] for more details. Some nonlinearities satisfying δQC will be listed.…”

“…As stated in [27], δQC can be described by a set of multiplier matrices which we call incremental multiplier matrices (δ MMs) in a particular form, and many other types of nonlinearities, such as Lipschitz, one-side Lipschitz, and incremental sector bound nonlinearities, can be rewritten in a unified form of δQC. Many references consider the control and observation problem for systems with nonlinearities satisfying δQC [26][27][28][29][30][31][32]. In [28], the authors proposed a secure chaotic communication scheme of chaotic systems which satisfy δQC.…”

“…In [28], the authors proposed a secure chaotic communication scheme of chaotic systems which satisfy δQC. In [31], full-order and reduced-order observers for discrete-time systems whose nonlinearities satisfy δQC are designed. Adaptive state observers are designed for incremental quadratically nonlinear systems in [32].…”

Stochastic stability and stabilization for stochastic differential semi‐Markov jump systems with incremental quadratic constraints

“…The researches on IQC have achieved some results. Açıkmeşe, 24 Zhao, 25 and Zhang 26 designed the observers for the nonlinear systems with IQC. Wang 27 considered the consensus protocol of nonlinear multi‐agent with IQC.…”

Observer‐based positive edge consensus for directed nodal networks

“…However, in many real circumstances, not all the state variables are available. Therefore, it motivates our further research on positive edge consensus via using the state observer [28–30]. In [22, 25], Su et al proposed a Luenberger observer‐based positive edge consensus protocol.…”