A small gain theorem for linear stochastic systems

DOI10.1016/S0167-6911(97)00008-XzbMath0901.93071WikidataQ127088811 ScholiaQ127088811MaRDI QIDQ1391599

Aristide Halanay, Adrian-Mihail Stoica, Vasile Dragan

Publication date: 22 July 1998

Published in: Systems \& Control Letters (Search for Journal in Brave)

zbMATH Keywords

stabilitystochastic systemssmall gainRiccati equations of stochastic controlinput-output norms

Mathematics Subject Classification ID

(H^infty)-control (93B36) Input-output approaches in control theory (93D25) Stochastic stability in control theory (93E15)

Related Items (16)

Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise ⋮ Global Stability of Feedback Systems with Multiplicative Noise on the Nonnegative Orthant ⋮ On detectability of stochastic systems ⋮ Vertex‐dependent filtering of retarded uncertain state‐multiplicative noisy systems ⋮ Stabilization of a class of stochastic nonlinear systems using a bang‐bang controller ⋮ Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing ⋮ Multiobjective $\mathcal{H}_2$/$\mathcal{H}_\infty$ Control Design Subject to Multiplicative Input Dependent Noises ⋮ Almost Sure Exponential Stability of Large-Scale Stochastic Nonlinear Systems ⋮ Robust vertex‐dependent H_∞ and H₂ estimation for stochastic linear systems ⋮ H_∞ preview tracking control of retarded state‐multiplicative stochastic systems ⋮ On unified concepts of detectability and observability for continuous-time stochastic systems ⋮ Static \(H_{2}\) and \(H_{\infty }\) output-feedback of discrete-time LTI systems with state multiplicative noise ⋮ \(H_{\infty}\)-like control for nonlinear stochastic systems ⋮ Robust stabilisation control for discrete-time networked control systems ⋮ Detectability, Observability, and Asymptotic Reconstructability of Positive Systems ⋮ Discussion on: ``An algorithm for solving a perturbed algebraic Riccati equation

Cites Work

• A course in \(H_{\infty}\) control theory
• State-feedback control of systems with multiplicative noise via linear matrix inequalities
• Feedback stabilizability for stochastic systems with state and control dependent noise
• A ``small gain theorem for time-varying systems
• Stability of regime-switching stochastic differential equations
• Bounded solutions of affine stochastic differential equations and stability
• Optimal stabilizing compensator for linear systems with state-dependent noise
• Stability radii of some time-varying linear stochastic differential systems
• Unnamed Item

This page was built for publication: A small gain theorem for linear stochastic systems