Steklov – Lyapunov type systems ∗
نویسندگان
چکیده
In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m) × so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized Gaudin form with a rational spectral parameter. In the case of rank 2 orbits a corresponding 2 × 2 Lax pair for the reduced systems enables us to perform a separation of variables.
منابع مشابه
A Lyapunov characterization of robust stabilization
One of the fundamental facts in control theory (Artstein’s theorem) is the equivalence, for systems affine in controls, between continuous feedback stabilizability to an equilibrium and the existence of smooth control Lyapunov functions. This equivalence breaks down for general nonlinear systems, not affine in controls. One of the main results in this paper establishes that the existence of smo...
متن کاملA fast method for distinguishing between ordered and chaotic orbits
Wedescribe a newmethod of distinguishing between ordered and chaotic orbits, which is much faster than the methods used up to now, namely (1) the distribution of the Poincaré consequents, (2) the Lyapunov characteristic number and (3) the distribution of the rotation angles. This method is based on the distribution of the helicity angles (the angles of small deviations ξ from a given orbit with...
متن کاملExtension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems
The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...
متن کاملConstruction of strict Lyapunov function for nonlinear parameterised perturbed systems
In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.
متن کاملFuzzy Lyapunov stability and exponential stability in control systems
Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...
متن کامل