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This paper considers a linear continuous- or discrete-time dynamic object in the absence of its mathematical model. As is demonstrated below, a control law that suboptimally damps initial and (or) exogenous disturbances of such objects can be implemented based on experimental and a priori data. The approach involves the methods of robust control design and duality theory as well as the technique of linear matrix inequalities. [ABSTRACT FROM AUTHOR]

The maximum output deviation of a linear time-varying system is defined as the worst-case measure of the maximum value of the output Euclidean norm over a finite horizon provided that the sum of the squared energy of an external disturbance and a quadratic form of the initial state is 1. Maximum deviation is characterized in terms of solutions to differential matrix equations or inequalities. A modified concept of the boundedness of the system on a finite horizon under an external and initial disturbances is introduced and its connection with the concept of maximum deviation is established. Necessary and sufficient conditions for the boundedness of the system on a finite horizon are obtained. It is demonstrated that optimal controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) as well as controllers ensuring the boundedness of the system can be designed using linear matrix inequalities. [ABSTRACT FROM AUTHOR]

The need for a game-theoretical formulation of the problem of linear-quadratic control under nonmeasurable plant state where the functional depends on the uncertain initial state was substantiated. The minimax output control law in terms of linear matrix inequalities that may be regarded as the optimal robust control law for the given set of the plant initial states was established assuming that the measurable components of the initial state were known and the nonmeasurable components take on values within the given ellipsoid. The results obtained were generalized to the plants with uncertain parameters. [ABSTRACT FROM AUTHOR]

We consider the synthesis of linear control laws under one integral and several phase constraints on the basis of the Lyapunov function method and the technique of linear matrix inequalities. In particular, our method permits one to obtain suboptimal state or output feedbacks providing the minimum upper bound for a quadratic functional under phase and control constrains or the minimum bound for the maximum deviation of the controlled variable under one integral and several phase constraints. The synthesis is generalized to the case of nonstationary parametric perturbations in the plant. [ABSTRACT FROM AUTHOR]

We suggest a new method for solving the stabilization problem under phase constraints with the use of linear matrix inequalities. We consider the cases of complete and incomplete state measurements and the presence of nonstationary parametric perturbations. In the synthesis of linear control laws, the suggested method permits one to cover all possible quadratic Lyapunov functions and indicate a set of initial values for trajectories satisfying the phase constraints. [ABSTRACT FROM AUTHOR]