Tracking and identification of regime-switching systems using binary sensors
Automatica (Journal of IFAC)
Randomly switching systems: models, analysis, and applications
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Stabilization of jump linear systems without noise
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Brief paper: Stability analysis of switched stochastic systems
Automatica (Journal of IFAC)
Stability of Regime-Switching Jump Diffusions
SIAM Journal on Control and Optimization
Brief The H2-control for jump linear systems: cluster observations of the Markov state
Automatica (Journal of IFAC)
Stability analysis and stabilization control of multi-variable switched stochastic systems
Automatica (Journal of IFAC)
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In this paper we first present an error analysis for the process of estimates generated by the Wonham filter when it is used for the estimation of the (finite set-valued) jump-Markov parameters of a random parameter linear stochastic system and further give bounds on certain functions of these estimates. We then consider a certainty equivalence adaptive linear-quadratic Gaussian feedback control law using the estimates generated by the nonlinear filter and demonstrate the global existence of solutions to the resulting closed-loop system. A stochastic Lyapunov analysis establishes that the certainty equivalence law stabilizes the Markov jump parameter linear system in the mean square average sense. The conditions for this result are that certain products of (i) the parameter process jump rate and (ii) the solution of the control Riccati equation and its second derivatives should be less than certain given bounds. An example is given where the controlled linear system has state dimension 2. Finally, the stabilizing properties of certainty equivalence laws which depend on (i) the maximum likelihood estimate of the parameter value and (ii) a modified version of this estimate are established under certain conditions.