In a typical cyber-physical system (CPS), the cyber/computation subsystem controls the physical subsystem, and therefore the computer society has recently paid considerable attention to CPS research. To keep such a CPS stable, feedback control with periodic computation tasks has been widely used, and its theoretical guarantee of stability has been made with periodic real-time task models that e...

A topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented. The stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points (and/or closed orbits) on the stability boundary. Several necessary and sufficient conditions are derived to determine...

This paper studies the local exact controllability and the local stabilization of the semilinear Schrödinger equation posed on a product of n intervals (n ≥ 1). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as fa...

A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers’ equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the ...

| In this note a continuous feedback control law with time-periodic terms is derived for the control of non-holonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector elds are homogeneou...

Sufficient conditions for uniform global asymptotic stabilization of the origin are obtained for bilinear control systems with periodic coefficients. The proof is based on the use of the Krasovsky theorem on global asymptotic stability of the origin for periodic systems. The stabilizing control function is feedback control constructed as the quadratic form of the phase variables and depends on ...

This work is concerned with the action of a semisimple element g of the semisimple connected Lie group Sl(d;R) on ag manifolds or F. These manifolds are obtained as left cosets of a parabolic group T. We consider minimal sets of g on F , assigning to each minimal set M an index K(M) which appears if one consider an special decomposition of the vector space R d related to g called the Conley Dec...

In this paper, sufficient criteria for the existence of multiple positive periodic solutions of a certain nonlinear dynamic system with feedback control are established. This is done by the Avery–Henderson fixed point theorem and the Leggett– Williams fixed point theorem. By using the method of coincidence degree, sufficient conditions are derived ensuring the existence of at least one periodic...

We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method...

In this study, a scheduling algorithm based on communication delay is proposed. This scheduling algorithm can tolerate delay of periodic communication tasks in wireless network control system. It resolves real-time problem of periodic communication tasks in wireless network control system and partly reduces overtime phenomenon of periodic communication tasks caused by delay in wireless network....