Observer-Based Sampled-Data Stabilisation of Switched Systems with Lipschitz Nonlinearities and Dwell-Time

2025/11/03 by Katz, Rami, Russo, Antonio, Incremona, Gian Paolo +2
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2511.01672

Abstract

We investigate the stabilisation of nominally linear switched systems with uncertain Lipschitz nonlinearities under dwell-time constraints, using a sampled-data switching law based on a state observer. We design the switching law based on Lyapunov-Metzler inequalities, accounting for the sampled-data output measurements, and we derive time-dependent LMI conditions for global asymptotic stability of the resulting closed-loop system. We obtain an estimate of the average quadratic cost and a bound on its maximum deviation from the actual cost. We also discuss the feasibility of the derived LMIs, provide equivalent reduced-order LMI conditions, and prove that the time dependence of the LMIs can be removed by discretising on a finite grid. Numerical examples illustrate our theoretical results.

Citations

• Stabilization of Switched Affine Systems With Dwell-Time Constraint
• An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control
• Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback
• Выпуклая оптимизация

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