A classification of generalised state space reduction methods for linear multivariable systems
A classification of linear controllable systems
A feedforward compensation scheme for perfect decoupling of measurable input functions
In this paper the exact decoupling problem of signals that are accessible for measurement is investigated. Exploiting the tools and the procedures of the geometric approach, the structure of a feedforward compensator is derived that, cascaded to a linear dynamical system and taking the measurable signal as input, provides the control law that solves the decoupling problem and ensures the internal stability of the overall system.
A functorial approach to the behaviour of multidimensional control systems
We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.
A general solution to the output-zeroing problem for MIMO LTI systems
The problem of zeroing the output in an arbitrary linear continuous-time system S(A,B,C,D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separately.
A hybrid domain analysis for systems with delays in state and control.
A Lyapunov functional for a system with a time-varying delay
The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays
A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.
A necessary and sufficient condition for normality of linear control system with delays
A new criterion for strong observability
A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models
In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization....
A new look at boundary perturbations of generators.
A new method for analytic determination of extremum of the transients in linear systems
A nonsmooth optimisation approach for the stabilisation of time-delay systems
This paper is concerned with the stabilisation of linear time-delay systems by tuning a finite number of parameters. Such problems typically arise in the design of fixed-order controllers. As time-delay systems exhibit an infinite amount of characteristic roots, a full assignment of the spectrum is impossible. However, if the system is stabilisable for the given parameter set, stability can in principle always be achieved through minimising the real part of the rightmost characteristic root, or...
A nonsmooth optimisation approach for the stabilisation of time-delay systems
This paper is concerned with the stabilisation of linear time-delay systems by tuning a finite number of parameters. Such problems typically arise in the design of fixed-order controllers. As time-delay systems exhibit an infinite amount of characteristic roots, a full assignment of the spectrum is impossible. However, if the system is stabilisable for the given parameter set, stability can in principle always be achieved through minimising the real part of the rightmost characteristic...
A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy
The question how the classical definition of the Smith zeros of an LTI continuous-time singular control system can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with a nonzero state-zero direction. Such a definition allows an infinite number of zeros (then the system is called degenerate). A sufficient and necessary condition for nondegeneracy is formulated. Moreover, some characterization of...
A note on the inversion of Sylvester matrices in control systems.
A pencil approach to high gain feedback and generalized state space systems
A pole assignment technique for multivariable systems with input delay
A polynomial solution to regulation and tracking. I. Deterministic problem