The LMI based method for the control with the state estimate, subject to the input variable constraints in the state feedback control of the linear MIMO systems, is presented in the paper. For this problem are obtained the state feedback as well as the estimator gain matrices that capture the required stability by solving the linear matrix inequalities formulated in the sense of the unified algebraic approach. The method is particularly effective when the input variable constraints and the system output are of interest.

The paper presents analysis of nonlinear response of a classical mechanical oscillator placed within a magnetic field and driven by a harmonic force. With an appropriate choice of control parameters, the system vibrates chaotically between different equilibrium positions. To prove this result, Lyapunov exponents have been calculated using the algorithm proposed by Rangarajan G., Habib S. and Ryne R.: Physical Review Letters, vol. 80, (1998). Moreover, the appropriate time series, phase portrait, Poincar'e cross-section and power spectrum are given to support the conclusion.

The paper addresses design problem of a robust parameter dependent quadratically stabilizing  output/state feedback model predictive control for linear polytopic systems without constraints using original equential approach.  The design procedure ensures stability, robustness properties  and guaranteed cost for the closed-loop uncertain system.

Vibrations control in truss structures reaches a great practical interest, mainly in modern structures of huge space vehicles and aircrafts. Two demands essences are required in design of such structures. The first is the excellent dynamic behavior, in order to guarantee the stability of the structure and high precision pointing. The second is the necessity to obtain light structures, in order to reduce the cost. However, these two requirements are often contradictory, because light structures have low degrees of internal damping, which hinders the accuracy requirements.

These difficulties can be overcome by applying recently developed advanced materials, as for instance piezoelectric materials. Several researchers have proved that piezoelectric material can effectively counteract the vibrations. Appropriate assurance active damping of these vibrations can be achieved by optimal location of the piezo elements in the structure.

It is proposed to place the actuators to maximize the mean value of energy transmitted from or dissipated by the actuators, while the sensor location should maximize the mean square value of system output, which also maximizes the signal-to-noise ratio. By using explicit expressions for controllability and observability grammians as well as modal energies, it is shown that the approaches based on the system responses to transient and persistent disturbances are closely related, and are equivalent for structures which damping is small and the natural frequencies of which are well spaced. The method of actuator and sensor optimal location via grammians was proposed and compared it with results given by the method of matrix norms.