In this work we derive an easily testable suffi- cient condition for assessing Almost Sure (AS) stability of a continuous-time Markov Jump Linear System (MJLS) with a finite state Markov form process. Such a condition is used to design a feedback stabilization strategy under the hypothesis that at least one mode is controllable. The proposed condition relies on some bounds on the 2-norm of the transition matrix over the time interval to the first jump. Such bounds are computed from the eigenvalues of the solutions of a set of associated Lyapunov equations, one for each mode. An algorithm is also given for designing the stabilizing feedback, based on a formulation of the sufficient condition in terms of an equivalent LMI problem.
On almost sure stabilization of continuous-time Markov Jump Linear Systems
TANELLI, MARA;BOLZERN, PAOLO GIUSEPPE EMILIO;COLANERI, PATRIZIO
2005-01-01
Abstract
In this work we derive an easily testable suffi- cient condition for assessing Almost Sure (AS) stability of a continuous-time Markov Jump Linear System (MJLS) with a finite state Markov form process. Such a condition is used to design a feedback stabilization strategy under the hypothesis that at least one mode is controllable. The proposed condition relies on some bounds on the 2-norm of the transition matrix over the time interval to the first jump. Such bounds are computed from the eigenvalues of the solutions of a set of associated Lyapunov equations, one for each mode. An algorithm is also given for designing the stabilizing feedback, based on a formulation of the sufficient condition in terms of an equivalent LMI problem.File | Dimensione | Formato | |
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