Technical reports

• "Topological entropy of nonlinear time-varying systems" (with D. Liberzon), 2026
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  We study the topological entropy of nonlinear time-varying systems. We establish conditions under which entropy is independent of the initial time and derive two general upper bounds based on the matrix measure of the system Jacobian and the spectral abscissa of a Metzler comparison matrix, respectively. A general lower bound is also obtained using the trace of the Jacobian. For interconnected systems, we first derive an upper bound using the matrix measure of an interconnection matrix constructed from the Jacobian blocks. We then establish a new upper bound based on the spectral abscissa of a Metzler comparison matrix, incorporating the interconnection structure through subsystem-wise trajectory-separation analysis. This bound also recovers the two general upper bounds as special cases. All bounds depend on asymptotic properties of the Jacobian over reachable sets or their convex hulls. Simple examples show that either general upper bound may be tighter, while a time-varying Lorenz system illustrates the effects of norm selection and subsystem decomposition.

• "Data-driven control of linear systems using quantized data" (with Z. Li), 2026
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  This paper studies data-driven stabilization of unknown discrete-time linear systems using only quantized state measurements that take values in finite sets. The proposed approach consists of two stages. In the controller design stage, we collect quantized data while maintaining a prescribed quantization error bound and use them to formulate a semidefinite program (SDP). We establish a verifiable condition under which any feasible solution to the SDP yields a stabilizing feedback gain, and show that a stabilizing gain can always be obtained when the quantization error is sufficiently small. In the stabilization stage, a Lyapunov-based quantizer update rule is developed to guarantee exponential convergence under quantized state feedback. As a key feature, the number of quantization cells remains finite in both stages and constant during stabilization. Simulation results illustrate the effectiveness of the proposed approach.

• "Input-to-state stabilization of linear systems under data-rate constraints" (with M. Zamani), 2026
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  We study feedback stabilization of linear systems under data-rate constraints in the presence of completely unknown disturbances. A communication and control strategy is proposed based on sampled and quantized state measurements, where the quantization range is dynamically adjusted using reachable-set approximations and a disturbance estimate derived from quantization parameters. The strategy alternates between stabilizing and searching stages to recapture the state after escapes from the quantization range. Under a data-rate condition, it guarantees input-to-state stability (ISS) with respect to the disturbance. An additional quantization symbol is introduced to establish ISS near the equilibrium. A simulation example illustrates the effectiveness of the proposed approach.

• "Topological entropy of switched nonlinear and interconnected systems" (with D. Liberzon and J. P. Hespanha), 2023
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  A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their active rates. A general lower bound is constructed as well, using a similar weighted average of lower limits of the traces of these Jacobian matrices. In a case of interconnected structure, the general upper bound is readily applied to derive upper bounds for entropy that depend only on "network-level" information. In a case of block-diagonal structure, less conservative upper and lower bounds for entropy are constructed. In each case, upper bounds for entropy that require less information about the switching signal are also derived. The upper bounds for entropy and their relations are illustrated by numerical examples of a switched Lotka–Volterra ecosystem model.