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Linear Switching Systems (linear + switching_system)

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Engineering100%

Selected Abstracts

Stability of Linear Parameter Varying and Linear Switching Systems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Fabian Wirth
We consider stability of families of linear time-varying systems, that are determined by a set of time-varying parameters which adhere to certain rules. The conditions are general enough to encompass on the one hand stability questions for systems that are frequently called linear parameter varying systems in the literature and on the other hand also linear switching systems, in which parameter variations are allowed to have discontinuities. Combinations of these two sets of assumptions are also possible within the framework studied here. Under the assumption of irreducibility of the sets of system matrices, we show how to construct parameter dependent Lyapunov functions for the systems under consideration that exactly characterize the exponential growth rate. It is clear that such Lyapunov functions do not exist in general. But every system of our class can be reduced to a finite number of subsystems for which irreducibility holds. [source]

Observer-based stabilization of linear switching systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2009
Paolo Caravani
Abstract The 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. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Stability of Linear Parameter Varying and Linear Switching Systems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Fabian Wirth
We consider stability of families of linear time-varying systems, that are determined by a set of time-varying parameters which adhere to certain rules. The conditions are general enough to encompass on the one hand stability questions for systems that are frequently called linear parameter varying systems in the literature and on the other hand also linear switching systems, in which parameter variations are allowed to have discontinuities. Combinations of these two sets of assumptions are also possible within the framework studied here. Under the assumption of irreducibility of the sets of system matrices, we show how to construct parameter dependent Lyapunov functions for the systems under consideration that exactly characterize the exponential growth rate. It is clear that such Lyapunov functions do not exist in general. But every system of our class can be reduced to a finite number of subsystems for which irreducibility holds. [source]