The present paper deals with observer design for discrete-time nonlinear descriptor systems. Through Finsler’s Lemma, we cut the link between the observer gains and the Lyapunov function, which relaxes existing conditions and introduces an extra degree of freedom. In addition, the results are expressed as LMI constraints. The effectiveness of the two proposed approaches is illustrated via sever...

A method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and...

For a generalized discrete–time system, possibly improper or polynomial, we give realization based formulas for the H2 optimal output feedback controller, under the same general hypotheses as in the proper case. The solution is provided in term of two descriptor algebraic Riccati equations and features the same elegant simplicity as the standard case.

A great interest is focused on driver assistance systems using the head pose as an indicator of the visual focus of attention and the mental state. In fact, the head pose estimation is a technique allowing to deduce head orientation relatively to a view of camera and could be performed by model-based or appearance-based approaches. Modelbased approaches use a face geometrical model usually obta...

Hankel norm and Nehari-type approximation problems arise in model reduction and H1-control theory. Existing solutions to the discrete-time version of these problems may be derived using a standard state-space framework, but the resulting solution formulas require an invertible A-matrix. As a further complication, the D-matrix in the representation formula for all solutions becomes unbounded in ...

This paper proposes a new representation for the predictor estimates recursion and corresponding Riccati equation for discrete-time, time-variant descriptor systems. The introduced “9-block” form for the predictor and Riccati equation presents an interesting simple and symmetric structure, which enable us to treat directly the most general systems where state and measurement noises are correlat...

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Conve...

This paper considers actuator-fault estimation for discrete-time descriptor systems with unknown but bounded system disturbance and measurement noise. A zonotopic fault estimation filter is designed based on the analysis of fault detectability indexes. To ensure estimation accuracy, the filter gain in the zonotopic fault estimation filter is optimized through the zonotope minimization. The desi...

We investigate the robust stabilization problem for the descriptor discrete-time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations over RH∞. Numerically reliable solutions are given for both the stability radius and the associated controller, which, in addition, regain the same simplicity as in ...

This paper deals with the H∞ recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to f...