Section: New Results

Observability And Observer Design For Nonlinear Systems

• In [18] a method to carried out the state estimation is proposed for a class of nonlinear systems with unknown inputs whose dynamics is governed by differential-algebraic equations (DAE). We achieve, under suitable conditions, to replace the original DAE for a system with differential equations only by using a zeroing manifold algorithm inducing a state space dimension reduction.

• In the paper [44] , we investigate the estimation problem for a class of partially observable nonlinear systems. For the proposed Partial Observer Normal Form (PONF), necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed PONF.

• Using the theory of non-commutative rings, the delay identification problem of nonlinear time-delay systems with unknown inputs is studied in the paper [82] . Necessary and sufficient conditions are proposed to judge the identifiability of the delay, where two different cases are discussed for the dependent and independent outputs, respectively. After that, necessary and sufficient conditions are given to analyze the causal and non-causal observability for nonlinear time-delay systems with unknown inputs.

• In the paper [58] , we investigate the stabilization of a linear plant subject to network constraints, partial state knowledge and time varying bounded parameter uncertainties. An event–triggered version of the Luenberger observer is proposed, and necessary conditions on the uncertainties are given in term of LMI's to enable output– based stabilization under different triggering strategies.

• The papers [47] , [76] investigate an unknown input observer design for a large class of linear systems with unknown inputs and commensurate delays. A Luenberger-like observer is proposed by involving only the past and actual values of the system output. The required conditions for the proposed observer are considerably relaxed in the sense that they coincide with the necessary and sufficient conditions for the unknown input observer design of linear systems without delays.

• The paper [71] deals with the problem to estimate some states of a multi-output nonlinear dynamical system which is partially observable. To address this problem, this paper provides a set of geometrical conditions that guarantee the existence of a change of coordinates which decomposes the studied nonlinear dynamical system into two dynamical subsystems, where the first one is of the well-known output injection form. This transformed form allows us to design a simple reduced-order (Luenberger-like) observer to estimate the observable state.