Unknown inputs observer design for descriptor systems with monotone nonlinearities

Abstract

Summary This paper is devoted to the reduced‐order unknown inputs observer design problem for a class of descriptor systems having generalized monotone nonlinearities. The underlying system is considered in general rectangular form with unknown inputs in dynamic and in output equations. Under some basic assumptions on system parameters, sufficient conditions for the existence of observers are proved by showing the stability of their error dynamics. The case where nonlinearity appears in output equation is also considered. The importance of the work is illustrated by real‐life and academic examples.

Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs—Application to secure communications

“…[24][25][26][27] A remarkable work has been done by Chakrabarty et al 21 where these nonlinearities have been studied on descriptor systems. Other types of nonlinearities usually being considered in observer design for descriptor systems are Lipschitz, 12,13,19,[28][29][30][31][32] which is the most common, one-sided Lipschitz, 33,34 monotone, [35][36][37] and quadratic inequality. 38 In the following section, Table 1 is given to establish the fact that these nonlinearities fall under the general case considered here.…”

“…Firstly, it has been reported in many cases that in practical applications, the measured output is not always a linear combination of the system states, but can also include nonlinear terms. 24,33,35,36 Thus, it is much more realistic to consider the existence of nonlinearities in the output. Secondly, in the specific application of secure communications that we consider, the inclusion of nonlinear terms in the transmitted output can enhance the complexity of the signal, and thus make the design more secure.…”

“…The purpose of considering output nonlinearities is twofold. Firstly, it has been reported in many cases that in practical applications, the measured output is not always a linear combination of the system states, but can also include nonlinear terms 24,33,35,36 . Thus, it is much more realistic to consider the existence of nonlinearities in the output.…”

Observers for differential-algebraic systems with Lipschitz or monotone nonlinearities

“…Recently, Gupta et al [19] presented a reduced-order observer design which is applicable to non-square DAEs with generalized monotone nonlinearities. Systems with nonlinearities which satisfy a more general monotonicity condition are considered in [40], but the results found there are applicable to square systems only.…”

“…It is our aim to present an observer design framework which unifies the above mentioned approaches. To this end, we use the approach from [7] for linear DAEs (which can be nonsquare) and extend it to incorporate both nonlinearities which are Lipschitz continuous as in [5,28] and nonlinearities which are generalized monotone as in [19,40], or combinations thereof. We show that if a certain LMI restricted to a subspace determined by the Wong sequences is solvable, then there exists a state estimator (or observer) for the original system, where the gain matrices corresponding to the innovations in the observer are constructed out of the solution of the LMI.…”