Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: In this paper, a Lyapunov-e direct method is used to find stabilizing state feedback laws for systems with uncertain state or control matrices, where the uncertainties are modelled as sector bounded non-linearities, and feedback laws ensuring global asymptotic closed loop stability are obtained using LyAPunov'e direct methods.
Abstract: Existence criteria and computational methods are presented for finding stabilizing state feedback laws for systems with uncertain state or control matrices. The uncertainties are modelled as sector bounded non-linearities, and feedback laws ensuring global asymptotic closed loop stability are obtained using Lyapunov'e direct method. The algorithms essentially amount to repeatedly solving a parameter dependent Riccati equation until the maximal solution becomes positive definite.
50 citations
TL;DR: In this paper, it was shown that a non-linear Fokker-Planck equation is the most general continuous asymptotic representation of master equations describing internal fluctuations in the limit of large systems.
Abstract: Using the theory of Markovian diffusion processes it is established that a non-linear Fokker-Planck equation is the most general continuous asymptotic representation of master equations describing internal fluctuations in the limit of large systems. The good agreement between the results of the Fokker-Planck approximation and those of the master equation description is demonstrated on several examples. The differences with van Kampen's approach are elucidated.
50 citations
TL;DR: In this article, the hidden symmetries of the modified Painleve-Ince equation were analyzed by transforming it to a third-order ODE, which is invariant under a three-parameter group by a Riccati transformation.
Abstract: The linearization and hidden symmetries of the modified Painleve–Ince equation, y‘+σyy’+βy3=0, where σ and β are constants, are presented. The linearization of this equation by a nonlocal transformation yields a damped (stable) or growing (unstable) harmonic oscillator equation for β≳0. Hidden symmetries are analyzed by transforming the modified Painleve–Ince equation to a third‐order ordinary differential equation (ODE) which, in general, is invariant under a three‐parameter group by a Riccati transformation. A type I hidden symmetry is found of a second‐order ODE found from the third‐order ODE where a symmetry is lost in the reduction of order by the non‐normal subgroup invariants. A type II hidden symmetry occurs in the third‐order ODE because the symmetries of a second‐order ODE, reduced from the third‐order ODE by another set of normal subgroup invariants, are increased.
50 citations
TL;DR: In this article, the stability radii of linear plants controlled by dynamic output feedback were characterized, and sufficient conditions for the existence of a compensator which achieves a suboptimal stability radius were derived.
Abstract: We consider linear plants controlled by dynamic output feedback which are subjected to blockdiagonal stochastic parameter perturbations. The stability radii of these systems are characterized, and it is shown that, for real data, the real and the complex stability radii coincide. A corresponding result does not hold in the deterministic case, even for perturbations of single-output feedback type. In a second part of the paper we study the problem of optimizing the stability radius by dynamic linear output feedback. Necessary and sufficient conditions are derived for the existence of a compensator which achieves a suboptimal stability radius. These conditions consist of a parametrized Riccati equation, a parametrized Liapunov inequality, a coupling inequality, and a number of linear matrix inequalities (one for each disturbance term). The corresponding problem in the deterministic case, the optimal $\mu$-synthesis problem, is still unsolved.
50 citations
TL;DR: A new time-domain method of quadratic-optimum control synthesis for systems described by linear finite-memory output predictors updated in real time is presented, leading to algorithms which are numerically robust and therefore suitable for real-time computation using microprocessors with reduced word length.
50 citations