Lie-Algebraic Stability Criteria for Switched Systems
SIAM Journal on Control and Optimization
Brief paper: Systematic ultimate bound computation for sampled-data systems with quantization
Automatica (Journal of IFAC)
Multisensor switching control strategy with fault tolerance guarantees
Automatica (Journal of IFAC)
Brief paper: Control design with guaranteed ultimate bound for perturbed systems
Automatica (Journal of IFAC)
Robust uniformly ultimate boundedness control for uncertain switched linear systems
Computers & Mathematics with Applications
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We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.