Stability radii of linear systems
Systems & Control Letters
Stability radius for structured perturbations and the algebraic Riccati equation
Systems & Control Letters
Stability radii of linear systems with respect to stochastic perturbations
Systems & Control Letters
Optimal control of switching diffusions with application to flexible manufacturing systems
SIAM Journal on Control and Optimization
Robust Stability of Linear Evolution Operators on Banach Spaces
SIAM Journal on Control and Optimization
Robust and optimal control
Stability Radii of Systems with Stochastic Uncertainty and Their Optimization by Output Feedback
SIAM Journal on Control and Optimization
H∞ -control for Markovian jumping linear systems with parametric uncertainty
Journal of Optimization Theory and Applications
SIAM Journal on Control and Optimization
Journal of Optimization Theory and Applications
Optimal Control for Continuous-Time Linear Quadratic Problems with Infinite Markov Jump Parameters
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Technical communique: Robust H2 control of continuous-time Markov jump linear systems
Automatica (Journal of IFAC)
Robust H2 control of Markovian jump systems with uncertain switching probabilities
International Journal of Systems Science
SIAM Journal on Control and Optimization
A decentralized H∞ routing control strategy for mobile networked multi-agents
ACC'09 Proceedings of the 2009 conference on American Control Conference
Automatica (Journal of IFAC)
Brief Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis
Automatica (Journal of IFAC)
Brief On robust stabilization of Markovian jump systems with uncertain switching probabilities
Automatica (Journal of IFAC)
A new perspective on the robustness of Markov jump linear systems
Automatica (Journal of IFAC)
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This paper addresses the robust stochastic stability and stabilization of continuous-time Markov jump linear systems (MJLS), with the Markov jump parameters taking values in a countably infinite set. It is assumed that the state and input matrices are subjected to norm-bounded uncertainty with a prespecified structure, which encompasses the block-diagonal setting. We introduce new robust analysis and synthesis characterizations such that, unlike previous approaches in the MJLS literature, the scaling parameters are treated as decision variables in linear matrix inequalities. As a by-product, new contributions to the theory of stability radii of MJLS are provided. When restricted to the finite case, we further introduce new adjoint linear matrix inequality (LMI) characterizations for each of the robust analysis and synthesis problems, as well as for stability radii. Besides the interest in its own right, the adjoint approach allows us to verify that, in the general MJLS case, there is a gap between the complex stability radius and what can be assessed with scaled versions of the small-gain theorem. This suggests a fundamental limitation of the robustness against linear perturbations that the H$_\infty$ control of MJLS may provide. Some numerical examples, which include the robust control of two interconnected oscillators, illustrate the main results.