Observer‐based stabilization of linear switching systems

Abstract

SUMMARYThe discrete component of the hybrid state of a discrete-time linear switching system is assumed to be uncontrolled and unobserved. Conditions of stabilizability for this class of systems are given in terms of a new definition of control invariance, based on the realization of a discrete observer that permits reconstruction of the discrete-state in certain intervals of the time basis. This paper highlights the relationship between the minimum dwell time of the system and its stabilizability. An almost complete characterization of stabilizability is offered in terms of certain subsets of the continuous-state space. These sets are amenable to tractable parametric procedures for controller synthesis.

Set-Theoretic Methods in Control

“…From a theoretical standpoint, the investigation based on set invariance is deeply applied to nonlinear systems [FAC10,BT11] and hybrid systems [DSDBP06,CDS09,BDSCD07,DS08]. Recent results in the definition and construction of probabilistic invariant sets are found in [CKRC11,KDDS12].…”

Continuous output integral sliding mode control for switched linear systems

“…[3][4][5]) that assume the state vector is available, and others that use only output information [6][7][8]. These strategies provide a nominal controller that makes the closed loop system to behave in a nominal way.…”

On stabilization and tracking for switching linear systems

“…in fault detection schemes where different modes are introduced to model possible faults in the plant. To the best of the authors' M. Baglietto knowledge, there are only few contributions which address the case where the knowledge of the plant configuration is not available, neither in real time nor with delay [10], [11], [12], [13]. Very recently, a paper [14] has considered the zero regulation problem for continuous-time MIMO switching linear systems with unknown switching signal.…”