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As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear...
The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.
This paper presents a novel family of Lyapunov-based controllers for the maximum power point tracking problem in the buck converter case. The solar power generation system here considered is composed by a stand-alone photovoltaic panel connected to a DC/DC buck converter. Lyapunov function candidates depending on the output are considered to develop conditions which, in some cases, can be expressed as linear matrix inequalities; these conditions guarantee that the output goes asymptotically to zero,...
The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing...
This paper presents a method to design explicit control Lyapunov functions for affine
and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”.
For these systems a positive definite function V0 is known that can only be made
non increasing by feedback. We describe how a control Lyapunov function can be
obtained via a deformation of this “weak” Lyapunov function. Some examples are
presented, and the linear quadratic situation is treated as an illustration.
The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for -attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of memoryless control problems in terms of Popov triplets...
This paper considers a design of variable structure with sliding mode controller for a class of uncertain dynamic system based on Singular Value Decomposition (SVD) method. The proposed method reduces the number of switching gain vector components and performs satisfactorily while the external disturbance does not satisfy the matching conditions. Subsequently the stability of the global system is studied and furthermore, the design of switched gain matrix elements based on fuzzy logic approach provides...
In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the...
In this work, we propose a methodology for the expression of necessary and
sufficient Lyapunov-like conditions for the existence of stabilizing
feedback laws. The methodology is an extension of the well-known Control
Lyapunov Function (CLF) method and can be applied to very general nonlinear
time-varying systems with disturbance and control inputs, including both
finite and infinite-dimensional systems. The generality of the proposed
methodology is also reflected upon by the fact that partial...
A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known...
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