The problem of analog system design for a minimal computer time has been formulated as the functional minimization problem of the control theory. The design process in this case is formulated as the controllable dynamic system. The optimal sequence of the control vector switch points was determined as a principal characteristic of the minimal-time system design algorithm. The different forms of...

The circuit optimization process is formulated as a dynamic controllable system. A special control vector is defined to redistribute the compute expense between a network analysis and a parametric optimization. This redistribution permits the minimization a computer time. The problem of a minimal-time circuit optimization can be formulated in this case as a classical problem of the optimal cont...

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...

We consider the Lyapunov equation for the linear dynamics, which arises naturally when one seeks for a Lyapunov function with a uniform, exact decrease. In this setting, a solution to the Lyapunov equation has been characterized only for quadratic Lyapunov functions. We demonstrate that the Lyapunov equation is a well-posed equation for strictly stable dynamics and a much more general class of ...

In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems ẋ = fσ(t,x), possessing a uniformly asymptotically stable equilibrium. Let ẋ = fp(t,x), p ∈ P, be the collection of the ODEs, to which the switched system corresponds. The number of the vector fields fp on the right-hand side of the differential equation is assumed to be finite...

The generalized methodology for electronic networks optimization was elaborated by means of the optimal control theory approach. A special control vector is defined to redistribute the compute expense between a network analysis and a parametric optimization. In this case the problem of the electronic system optimization is formulated as a classical problem of functional minimization of the opti...

Lyapunov functions are an important tool to determine the basin of attraction of exponentially stable equilibria in dynamical systems. In Marinosson (2002), a method to construct Lyapunov functions was presented, using finite differences on finite elements and thus transforming the construction problem into a linear programming problem. In Hafstein (2004), it was shown that this method always s...

Nonlinear tracking control of unmanned underwater vehicles (UUVs) in 6 degrees of freedom (DOF) is discussed. The 4-parameter unit quaternion is used in a singularity-free representation of attitude. Several control laws based on a generalized Lyapunov function for the attitude dynamics are derived, including feedback from the vector quaternion, the Euler rotation vector and the Rodrigues param...