In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic quadratic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are...

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An expl...

A dynamical system describes the consequence of current state an event or particle in future. The models expressed by functions systems are more often deterministic, but these might also be stochastic some cases. prediction system's behavior future is studied with analytical solution implicit relations (Differential, Difference equations) and simulations. discrete-time first order equations qua...

A particular class of uncertain linear discrete-time periodic systems is considered. The problem of robust stabilization of real polytopic linear discrete-time periodic systems via a periodic state-feedback control law is tackled here, along with H2 performance optimization. Using additional slack variables and the periodic Lyapunov lemma, an extended sufficient condition of robust H2 stabiliza...

This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and coefficient with Lipschitz continuity, first two is established, an explicit rate derived third semi-discretization. The semi-discretization applied to linear quadratic control problem, temporally semi-discrete approximation optimal es...

Stochastic control design techniques found in the chemical process control literature generally focus on the reduction of state or output variance to improve process operation. Most of these techniques address the problem of minimizing a quadratic cost function subject to linear process dynamics. In these cases, a linear feedback control law results and the disturbance, state and output PDF’s a...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

A problem of robust state feedback stability and stabilization of nonlinear discrete-time stochastic processes is considered. The linear rate vector of a discrete-time system is perturbed by a nonlinear function that satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of nonlinear discrete-time systems and, at the...