By introducing the notations of dissipative and strictly dissipative p-symmetrizers of initial-boundary-value problems for linear hyperbolic systems we formalize the dissipative integrals technique [A. Blokhin, Yu. Trakhinin, in Handbook of Mathematical Fluid Dynamics, Vol. 1, North-Holland, Amsterdam, 2002, pp. 545–652] applied earlier to shock waves and characteristic discontinuities for vari...

The area of analysis and control of linear parameter-varying (LPV) systems has received much recent attention because of its importance in developing systematic techniques for gain-scheduling. An LPV system resembles a linear system that nonlinearly depends on one or more time-varying parameters. Nonlinear systems are often modeled in the LPV system via the parameterized Jacobian linearization....

We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with ...

We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative...

The problem of delay-dependent dissipative analysis and control for stochastic singular systems with state delay is investigated in this paper. Delay-dependent dissipative condition for the stochastic singular systems with state delay is obtained by employing singular stochastic Lyapunov and LMI-based methods. Based on this condition, a delay-dependent dissipative controller is presented. A num...

This paper considers the problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodele...

In this paper an approach is proposed to introduce Hamiltonian formalism to dissipative mechanical systems. This approach is based upon below viewpoints proposed in this paper: under a certain identical initial condition a dissipative mechanical system shares a common phase flow curve with a conservative system; the Hamiltonian of the conservative system is the value of the total energy of the ...