In this paper, Gain-Scheduling (GS) control via parameter dependent Lyapunov function for crane is synthesized. A purpose of cranes system is to lift and carry a load to assigned positions. Cranes are required to transport the load fast, accurately and to reduce oscillations. In previous research, a method to robust control of cranes to suppress effects by variation of the rope length have been...

In this paper, we use a state-dependent Lyapunov function to reduce the conservatism in stability analysis of Takagi-Sugeno (T-S) fuzzy systems via Linear Matrix Inequalities (LMIs). Our approach uses T-S fuzzy rules to deene Lyapunov functions, and therefore substantially enlarges the class of Lyapunov functions which can be used to prove stability of T-S fuzzy systems. This approach greatly r...

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the inputto-state stability of a system. Then for the case of the systems described by abstract equations in Banach spaces we develop two methods of construction of local and global I...

The paper deals with the stability properties of linear discrete-time switched systems with polytopic sets of modes. The most classical way of studying the uniform asymptotic stability of such a system is to check for the existence of a quadratic Lyapunov function. It is known from the literature that letting the Lyapunov function depend on the time-varying switching parameter improves the chan...

We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that th...

This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results. Keywords—Switched system,...

We consider nonlinear systems dx=dt = f(x(t)) where Df(x(t)) is known to lie in the convex hull of L matrices A1, : : : , AL 2 R n . For such systems, quadratic Lyapunov functions can be determined using convex programming techniques [1]. This paper describes an algorithm that either nds a quadratic Lyapunov function or terminates with a proof that no quadratic Lyapunov function exists. The alg...

Based on a geometrical method, the internal relationships between locally parameterized curves and the local parameterized surfaces are analyzed. A necessary and sufficient condition is derived for the local convexity of parameterized surfaces and functional surfaces. A criterion for local convexity (concavity) of parameterized surfaces is found, also, the criterion condition of binary function...