Abstract
Global quadratic stabilization in probability is considered for both switched linear certain stochastic systems and switched linear uncertain stochastic systems where there are norm bounded uncertainties. Under the assumption that every single subsystem is NOT globally quadratically stable in probability (GQS-P), we propose both static and dynamic output based switching laws such that the switched system on hand is GQS-P. In the case of static output based switching, the condition is expressed by a set of matrix inequalities, while the design of dynamic output based switching is proposed with a convex combination of subsystems and a robust Luenberger observer for each subsystem. Numerical examples are presented to show validity of the design conditions and switching algorithms.
Highlights
INTRODUCTIONSwitched systems consist of a set of subsystems, which are continuous-time or discrete-time, and a switching law (or, switching rule/strategy/signal) specifying one subsystem which will be activated for any time instant
Switched systems consist of a set of subsystems, which are continuous-time or discrete-time, and a switching law specifying one subsystem which will be activated for any time instant
The discussion is extended to switched linear uncertain stochastic systems (SLUSS) with norm bounded uncertainties, with the sufficient condition updated by dealing with the uncertainty terms
Summary
Switched systems consist of a set of subsystems, which are continuous-time or discrete-time, and a switching law (or, switching rule/strategy/signal) specifying one subsystem which will be activated for any time instant. Motivated by the above mentioned observation, we here aim to design output based switching laws for quadratic stabilization of switched linear stochastic systems, under the assumption that no single subsystem is GQS-P. We first consider switched linear certain stochastic systems (SLCSS), and propose a sufficient design condition and an output based switching law such that the resultant switched system is GQS-P. The discussion is extended to switched linear uncertain stochastic systems (SLUSS) with norm bounded uncertainties, with the sufficient condition updated by dealing with the uncertainty terms. This remaining part of this paper is organized as follows. We formulate our control problem as follows: For the SLCSS (15) and the SLUSS (16), design the output based switching law σ (y), such that the resultant switched systems are GQS-P
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