Search

In this paper, the controllability and observability of linear time-invariant uncertain systems are investigated. The systems under consideration contain time-invariant uncertain parameters that may take arbitrarily large values. In such a situation, the locations of uncertain parameters in system matrices play an important role. We examine the permissible locations of uncertain parameters in system matrices for a linear uncertain system to be controllable and observable independently of the bounds of the uncertain parameters. The objective of this paper is to show that a linear uncertain system is controllable and observable, irrespective of the bounds of uncertain parameters, if and only if the system has a particular configuration called a complete generalized antisymmetric stepwise configuration (CGASC). Furthermore, the dual configuration of a CGASC is introduced and studied here. [ABSTRACT FROM AUTHOR]

In this note, the model reduction problem for a class of discrete-time switched linear parameter varying systems under average dwell time switching is investigated. A parameterized reduced-model is constructed and the corresponding existence conditions of such models are derived via strict LMI formulation. The minimal average dwell time among all the subsystems and the desired reduced system are obtained such that the resulting model error system is exponentially stable and has a guaranteed l2 - l∞ error performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this note, we establish a set of conditions under which an ellipsoid is contractively invariant with respect to a singular linear system under a saturated linear feedback. These conditions can be expressed in terms of linear matrix inequalities, and the largest contractively invariant ellipsoid can be determined by solving an optimization problem with LMI constraints. With the feedback gain viewed as an additional variable, this optimization problem can be readily adapted for the design of feedback gain that results in the largest contractively invariant ellipsoid. Moreover, in the degenerate case where the singular linear system reduces to a regular system, our set invariance conditions reduce to the existing set invariance conditions for normal linear systems. [ABSTRACT FROM AUTHOR]

Under the assumption that the regulation error is the only feedback signal, it is shown how to design a global regulator capable of rejecting and/or tracking signals made of at most m sinusoidal terms with unknown frequencies, magnitudes, and phases for linear observable minimum phase systems. The asymptotic convergence of the tracking error to zero is guaranteed provided that an upper bound is known on the number of sinusoidal terms, even though the values of the unknown frequencies may not be recovered. Exponential convergence is achieved if all the exosystem frequencies are excited. [ABSTRACT FROM AUTHOR]

This note studies the performance limitation of a feedback system with a given linear time-invariant (LTI) plant in tracking a sinusoidal signal. It continues and goes beyond some recent studies in the same topic in which it is assumed that the controller can access all the past and future values of the reference signal. In this note, we consider the more realistic (and more difficult) situation where the controller only accesses the current and past values of the reference. An explicit formula of the best attainable performance is obtained for a single-input-single-output (SISO) system which depends on the nonminimum phase zeros of the plant and the frequency of the reference sinusoid. Compared to the previously studied case when the future of the reference is available, this formula clearly shows the extra effort one has to pay due to the lack of the reference information. A partial result for a multiple-input-multiple-output (MIMO) system is also given. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of stabilization of uncertain systems in the presence of input constraint First algebraic conditions are derived for input-to-state stability of linear system with saturated linear feedback of low dimension. Then a recursive design procedure is derived for robust stabilization of block upper triangular nonlinear systems with feedforward structure. [ABSTRACT FROM AUTHOR]

Fair synthesis of supervisory control for discrete-event systems is discussed. It is argued that a least restrictive supervisor does not in general exist unless a bound is placed on the number of transitions before which a desired event is required to happen. It is shown how such bounded fairness can be implemented using first-input-first-output (FIFO) queues. Although the language generated by a queue is not the largest among bounded fair restrictions of a behavior, nonoptimality can be exploited in hierarchical implementation of queues by grouping a subset of subsystems as a team and designing two modular queues: one to implement fairness locally among the team members, and the other to implement fairness globally between the team and other subsystems. [ABSTRACT FROM AUTHOR]

A nonstandard singularly perturbed linear time-invariant system with a general type of small delay in state and control variables is considered. Two much simpler parameter-free systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. Since the original system is nonstandard, the reduced-order one is descriptor (differential-algebraic). A composite feedback control exponentially stabilizing the original system is constructed based on stabilizing controls of the reduced-order and boundary-layer systems. An illustrative example is presented. [ABSTRACT FROM AUTHOR]

In the above paper, an approach was proposed for the disturbance decoupling for the linear system. Some details in the proof of the sufficiency of Theorem 2 for the existence of the matrix F1 are omitted. In this note, we will give a detailed proof. [ABSTRACT FROM AUTHOR]