Design of observers for switched discrete-time linear systems

Abstract

An approach to estimation based on Luenberger-like observers is considered for a class of switched discretetime linear systems. Three observers are proposed. The first one is based only on the satisfaction of stability conditions for the error dynamics, which can be expressed by means of Linear Matrix Inequalities (LMIs). The second observer is basically the first one but its design is accomplished by minimizing an upper bound on a quadratic cost function of the estimation error using LMI-based optimization techniques. The third observer differs from the previous ones as it is constructed by using a projection technique. Simulation results are reported to show the effectiveness of the proposed estimation methods.

High-order sliding mode observers for nonlinear autonomous switched systems with unknown inputs

“…The main difference is related to the knowledge of the active discrete state or operating mode: some approaches consider only continuous state uncertainty with known operating mode, while others assume that both the operating mode and the continuous state are unknown. In Alessandri and Coletta [1] and Bejarano et al [7] a Luenberger observer approach and a high-order sliding-mode observer for linear systems are proposed for the known operating mode case. Another work considering the operating mode is known and that the output and input are available is the one presented by Pina and Botto [29].…”

Design of Observers with Commutation-Dependent Gains for Linear Switching Systems

“…In [2], [13], an approach was proposed that consists in finding discrete-state-dependent observer gains that admit a common Lyapunov function for the error dynamics. According to such an approach, the observer takes on the form…”

“…Assuming the knowledge of λ t , the dynamics of the estimation error e t △ = x t −x t behaves like a switching system and a common Lyapunov function can be searched in order to ensure the stability of the estimation error. In [2], [13], a quadratic Lyapunov function of the form V (e t ) = e ⊤ t P e t with P > 0, was considered.…”

“…In [2], [13], under the assumption of a perfect knowledge of the switching times and modes, the problem of constructing observers for switching systems was faced by suitably extending the classical Luenberger observer to take into account the different system modes. Such an approach consists in finding mode-dependent observer gains that admit a common quadratic Lyapunov function for the error dynamics.…”

Development of a simultaneous continuum and noncontinuum state estimator with application on a distillation process

“…Alessandri and Coletta 7,8 considered an estimation approach based on Luenberger-like observers for a class of switched continuous and discrete time linear systems with a known operating mode. Böker and Lunze 9 proposed switching Kalman filters for switched affine systems, where a set of Kalman filters is designed for each local dynamics of the hybrid system.…”