Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1901.08513

Finite-Time Stability of Switched and Hybrid Systems with Unstable Modes

Kunal Garg·Dimitra Panagou
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we study finite-time stability of switched and hybrid systems in the presence of unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of the system to be finite time stable. More specifically, we show that even if the value of the Lyapunov function increases in between two switches, i.e., if there are unstable modes in the system, finite-time stability can still be guaranteed if the finite time convergent mode is active long enough. In contrast to earlier work where the Lyapunov functions are required to be decreasing during the continuous flows and non-increasing at the discrete jumps, we allow the Lyapunov functions to increase \emph{both} during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the earlier results in the related literature, and in effect allow the hybrid system to have unstable modes. Then, we illustrate how the proposed finite-time stability conditions specialize for a class of switched systems, and present a method on the synthesis of a finite-time stabilizing switching signal for switched linear systems. As a case study, we design a finite-time stable output feedback controller for a linear switched system, in which only one of the modes is controllable and observable. Numerical example demonstrates the efficacy of the proposed methods.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kunal Garg, Dimitra Panagou. 2019-12-17. Finite-Time Stability of Switched and Hybrid Systems with Unstable Modes. https://arxiv.org/abs/1901.08513

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Co-Investment with Payoff-Sharing Mechanism for Cooperative Decision-Making in Network Design Games

Network-based systems are inherently interconnected, with the design and performance of subnetworks being interdependent. However, the decisions of self-interested operators may lead to suboptimal outcomes for users and the overall system. This paper explores cooperative mechanisms that can simultaneously benefit both operators and users. We address this challenge using a game-theoretical framework that integrates both non-cooperative and cooperative game theory. In the non-cooperative stage, we propose a network design game in which subnetwork decision-makers strategically design local infrastructures. In the cooperative stage, co-investment with payoff-sharing mechanism is developed to enlarge collective benefits and fairly distribute them. To demonstrate the effectiveness of our framework, we conduct case studies on the Sioux Falls network and real-world public transport networks in Zurich and Winterthur, Switzerland. Our evaluation considers impacts on environmental sustainability, social welfare, and economic efficiency. The proposed framework provides a foundation for improving interdependent networked systems by enabling strategic cooperation among self-interested operators.

eess.SY↗
arXiv2026

Generalizable Optimal Control with Transformers: One Policy Across Diverse Systems

Classical optimal control designs a separate controller for each plant. Even for the Linear Quadratic Regulator (LQR), every new model must be identified and its Riccati equation re-solved. We ask whether a single learned policy can instead serve an entire family of systems, and we show that one transformer can. We train the policy to imitate optimal LQR state feedback across a collection of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems that differ in their state and input dimensions and in their cost objectives. A shared representation lets the same parameters control every member of the family. It combines system-wise standardization, zero-padding and masking across dimensions, and an explicit encoding of the cost matrices. At run time, the policy maps a short window of recent states and the specified cost to a control action. It uses no plant matrices and identifies the dynamics implicitly from the state history. We evaluate on $28$ simulated systems over $9{,}675$ closed-loop rollouts, and no unstable rollout was observed in any of them. On the systems seen during training, it attains a median relative sub-optimality of $0.022\%$, even under parameter perturbations of up to $\pm10\%$. It transfers to unseen systems with lightweight fine-tuning, reaching a median sub-optimality of $0.19\%$. These results support transformers as generalizable near-optimal controllers for structured families of linear systems.

eess.SY↗
arXiv2026

Two-Timescale Asymptotic Simulations of Hybrid Inclusions with Applications to Stochastic Hybrid Optimization

Convergence properties of model-free two-timescale asymptotic simulations of singularly perturbed hybrid inclusions are developed. A hybrid inclusion combines constrained differential and difference inclusions to capture continuous (flow) and discrete (jump) dynamics, respectively. Sufficient conditions are established under which sequences of iterates and step sizes constitute a two-timescale asymptotic simulation of such a system, with limiting behavior characterized via weakly invariant and internally chain-transitive sets of an associated boundary layer and reduced system. To illustrate the applicability of these results, conditions are given under which a two-timescale stochastic approximation of a hybrid optimization algorithm asymptotically recovers the behavior of its deterministic counterpart.

eess.SY↗