This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc condition...

We consider the problem of state and parameter reconstruction for uncertain dynamical systems that cannot be transformed into the canonical adaptive observer form. The uncertainties are allowed to be both linearly and nonlinearly parameterized functions of state and time. We provide a technique that allows successful reconstruction of uncertain state and parameters for a broad range of dynamica...

This paper addresses the position tracking control problem of an underactuated hovercraft vehicle. A nonlinear Lyapunov-based tracking controller is developed and proved to exponentially stabilize the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be a specially chosen trajectory (e.g., a trimming trajectory). ...

This paper examines the problems of robust H∞ filtering design for linear parameter-varying discrete-time systems with time-varying state delay. We present new H∞ performance criteria that depend on the parameters and the delay-varying magnitude using appropriately selected Lyapunov-Krasovskii functional. Then the corresponding filter can be obtained from the solution of convex optimization pro...

Local output feedback stabilization with smooth nonlinear controllers is studied for parameterized nonlinear systems of which the linearized system possesses multiple pairs of imaginary eigen-values, and the bifurcated solution is unstable at the critical value of the parameter. Necessary and suucient conditions are sought for stabilization of such nonlinear bifurcated systems based on the proj...

Closed physical systems eventually come to rest, the reason being that due to friction of some kind they continuously lose energy. The mathematical extension of this principle is the concept of a Lyapunov function. A Lyapunov function for a dynamical system, of which the dynamics are modelled by an ordinary differential equation (ODE), is a function that is decreasing along any trajectory of th...

2 PARAMETERIZED MODULES AS PARAMETERS A feature of OBJ3 not discussed in [8] allows the use of parameterized modules as parameter theories of other modules. The example below follows one suggested by Yatsu and Futatsugi [9] in connection with their design work on the CafeOBJ system [2]. The parameterized LIST object defines lists, with a comma syntax for concatenation. The theory FUN defines an...

In this study, we prove that a countably infinite number of one-parameterized one-dimensional dynamical systems preserve the Lebesgue measure and are ergodic for measure. The consider connect parameter region in which exact one almost all orbits diverge to infinity correspond critical points weak chaos tends occur (the Lyapunov exponent converging zero). These results generalization work by Adl...

This paper focuses on the design of control Lyapunov function for control affine systems to guarantee the stability for the states of interest in a specified region. Without restrictive assumptions found in previous approaches, a min-max optimization problem is formulated to solve for a quadratic Lyapunov function. A derivative-free coordinate search method is employed to optimize a non-differe...

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...