arXiv subjects

Chung-Yao Kao

Publications and source records attributed to Chung-Yao Kao.

8 recordsLinked to original sources

arXiv2026

Partitioned robustness analysis of networks with uncertain links

Network robustness to link perturbations is studied from an input-output perspective. The main result is a set of integral quadratic constraints (IQCs) that imply robust stability of the uncertain network dynamics. The model dependency of each IQC is localized according to an overlapping edge-partition for the network graph. The choice of partition over the admissible set affords flexibility in balancing conservativeness of the distributed certificate against its verification complexity. This is illustrated by a numerical example for a network with sampled-data links.

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arXiv2026

Exact Robust Instability Analysis for Networked Dynamical Systems with Biological Application

This paper investigates robust instability in nominally unstable uncertain networked dynamical systems, where all nominal agents share an identical single-input-single-output (SISO) linear time-invariant (LTI) system and each agent is subject to independent perturbations. This setting is motivated by the problem of sustaining periodic oscillations in nonlinear dynamics, for which exact analysis is generally intractable. We identify three classes of network structures including cyclic and certain rank-deficient networks for which the robust instability problem can be reduced to the analysis of a single representative SISO system. We derive sufficient conditions that exactly characterize the robust instability radius for these network classes. Finally, we demonstrate the practical utility of the proposed results by analyzing oscillatory behavior in a genetic regulatory network.

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arXiv2026

Robust Instability Radius for Networked Dynamical Systems: Upper and Lower Bounds

This paper is concerned with robust instability of uncertain network systems. We consider the multi-agent system described as a network of single-input-single-output agents with identical nominal dynamics subject to heterogeneous perturbations. The network description is formalized as a feedback interconnection of a diagonal uncertainty, nominal identical agents, and a static interconnection matrix. Assuming that the nominal network is unstable, we seek the robust instability radius (RIR), defined as the smallest norm of the stable uncertainty that renders the network stable. Conditions for the network stability are developed, and upper and lower bounds on the RIR are derived. When the network connectivity matrix is rank one and all diagonal entries share the same sign or are zero, we give conditions under which the RIR is exactly characterized by a small gain argument.

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arXiv2024

Exact Instability Radius of Discrete-Time LTI Systems

The robust instability of an unstable plant subject to stable perturbations is of significant importance and arises in the study of sustained oscillatory phenomena in nonlinear systems. This paper analyzes the robust instability of linear discrete-time systems against stable perturbations via the notion of robust instability radius (RIR) as a measure of instability. We determine the exact RIR for certain unstable systems using small-gain type conditions by formulating the problem in terms of a phase change rate maximization subject to appropriate constraints at unique peak-gain frequencies, for which stable first-order all-pass functions are shown to be optimal. Two real-world applications -- minimum-effort sampled-data control of magnetic levitation systems and neural spike generations in the FitzHugh--Nagumo model subject to perturbations -- are provided to illustrate the utility of our results.

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arXiv2023

Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization -- phase change rate maximization --

This paper is concerned with a new optimization problem named "phase change rate maximization" for single-input-single-output linear time-invariant systems. The problem relates to two control problems, namely robust instability analysis against stable perturbations and minimum-norm strong stabilization. We define an index of the instability margin called "robust instability radius (RIR)" as the smallest $H_\infty$-norm of a stable perturbation that stabilizes a given unstable system. This paper has two main contributions. It is first shown that the problem of finding the exact RIR via the small-gain condition can be transformed into the problem of maximizing the phase change rate at the peak frequency with a phase constraint. Then, we show that the maximum is attained by a constant or a first-order all-pass function and derive conditions, under which the RIR can be exactly characterized, in terms of the phase change rate. Two practical applications are provided to illustrate the utility of our results.

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arXiv2023

On Phase Change Rate Maximization with Practical Applications

We recapitulate the notion of phase change rate maximization and demonstrate the usefulness of its solution on analyzing the robust instability of a cyclic network of multi-agent systems subject to a homogenous multiplicative perturbation. Subsequently, we apply the phase change rate maximization result to two practical applications. The first is a magnetic levitation system, while the second is a repressilator with time-delay in synthetic biology.

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arXiv2021

Converse Theorems for Integral Quadratic Constraints

A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is stable, then the given system must necessarily satisfy the complementary IQC. These theorems are specialized to derive multiple versions of converse passivity results. They cover standard notions of strict passivity as well as passivity indices that characterize the trade-offs between passivity surplus and deficit. Converse frequency-weighted small-gain and passivity theorems are also established.

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arXiv2020

Integral quadratic constraints for asynchronous sample-and-hold links

A model is proposed for a class of asynchronous sample-and-hold operators that is relevant in the analysis of embedded and networked systems. The model is parametrized by characteristics of the corresponding time-varying input-output delay. Uncertainty in the relationship between the timing of zero-order-hold update events at the output and the possibly aperiodic sampling events at the input means that the delay does not always reset to a fixed value. This is distinct from the well-studied synchronous case in which the delay intermittently resets to zero at output update times. The main result provides a family of integral quadratic constraints that covers the proposed model. To demonstrate an application of this result, robust $\mathbf{L}_2$ stability and performance certificates are devised for an asynchronous sampled-data implementation of a feedback loop around given linear time-invariant continuous-time open-loop dynamics. Numerical examples are also presented.

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