New proof for Kalman's criterion of state controllability

A new proof is given for Kalman's criterion of state controllability in linear time-invariant dynamical systems. The proof is constructive, in that it may be used to generate control strategies.     

Alternative Kalman controllability criterion for nonderogatory systems

Kalman's controllability matrix with multiple controls is rearranged to yield a different form of the controllability matrix for nonderogatory systems. The result is proved by expanding the modal forms of the controllability matrices.     

Testing the controllability of linear time-invariant systems

A method for studying the controllability of a linear time-invariant system by considering the controllability of a smaller subsystem is proposed. The method is most effective when the system under study has a large number of inputs and states.     

Local controllability and minimum energy control of continuous 2-D linear systems with variable coefficients

Necessary and sufficient conditions for the local controllability of continuous 2-D linear systems with variable coefficients are established. The minimum energy control problem is formulated and solved for the 2-D systems.     

Control of linear systems with time delay

Luenberger's procedure for the design of controllers of linear systems with inaccessible state vectors is extended to deal with time-delay systems.     

Improved stability criterion for uncertain stochastic delay systems with nonlinear uncertainties

Based on an integral inequality, a stability criterion for uncertain stochastic delay systems with nonlinear uncertainties is obtained in terms of a linear matrix inequality. The restriction used to bound some trace term in the existing methods is removed. The advantage of the proposed method is verified by a numerical example.     

On Hautus-type conditions for controllability of implicit linear discrete-time systems

Four notions of controllability for general (i.e., possibly nonregular) implicit linear discrete-time systems are considered. Relationships between them are studied. A Hautus-type characterization of all of these notions is also given.This work was performed under the auspices of RP.I.02: Teoria sterowania i optymalizacji ciagych ukadów dynamicznych i procesów dyskretnych.     

A new criterion for investigating the characteristics of linear systems

A criterion which guarantees complete controllability and complete observability of linear systems is derived. It is shown that if the output covariance of the system, when excited by stationary white noise, be separable and the components of the separating vectors be linearly independent, then the system is completely controllable and observable. This criterion is specially significant in designing shaping filters, or whitening filters when the only known information is the output covariance of the system.     

Simple proof of the Simon-Mitter controllability theorem

It is shown that the introduction of generalised mode-controllability matrices of multivariable time-invariant linear systems greatly facilitates a simple and direct proof of the Simon?Mitter theorem concerning the controllability characteristics of such systems. This proof is presented for systems whose plant matrices have any Jordan canonical form.     

Stability of constant coefficient linear singular systems with delay

In this paper, the general class of singular systems with delay and linear constant coefficient singular systems with delay are discussed. First, several definitions of stability are presented for singular systems with delay, and general sufficient stability conditions and instability conditions are obtained. Second, stability and instability are analyzed for linear constant coefficient singular systems with delay.This project was supported by the Guangdong Provincial Natural Science Foundation of China, No. 990584.     

Stability of control systems with time delay

To find the approximate stability limit on the forward gain in control systems with small time delay, this note suggests approximating the exponential in the characteristic equation by the first few terms of its series and using the Routh?Hurwitz criterion. This approximation avoids all the time-consuming graphical work and gives a somewhat pessimistic maximum bound for the gain constant.     

Calculation of piecewise-constant control strategies for linear systems with retarded control

The letter presents a simple method of calculating piecewise-constant control strategies to transfer the state of a linear time-invariant system with retarded control from a given initial state xo to any desired state x(t*), provided that the system is controllable.     

Smith-fuzzy fractional control of systems with time delay

The fractional calculation is over 300 years old, but only in the last decades its application arisen in many areas of science and engineering. The explanation for this expansion in the scientific and tecnologic worlds is due to the good results obtained in solving different problems, which have overcome the classics. On the other hand, in the control area there was an increasing interest in the development of new strategies, which resulted in new algorithms where the use of the fractional calculus revealed an helpfull tool. In this paper we apply the fractional order concepts into two systems with time delay. Several algorithms are investigated and compared, when integrated within a Smith predictor structure and with an optimal fuzzy fractional PD^β+I controller in which the parameters are tuned by a genetic algorithm. Simulations are presented assessing the performance of the proposed fractional schemes.     

Simple proof of unconditional controllability and observability

A direct proof using a frequency-domain argument is given of Chu's theorem on complete controllability and observability for every nonzero input and output matrix.     

Geometric criterion for the absence of limit cycles in nonlinear control systems

In most autonomous systems, the generation of periodic modes is considered to be an instability. Considering feedback systems composed of a time-invariant linear operator in cascade with an odd memoryless nonlinearity, a method is derived which provides a geometric interpretation of frequency regions in the Nyquist plane, over which simple oscillations cannot occur. This criterion answers a question of system behaviour when the Popov criterion is violated.     

Stability of a class of linear switching systems with time delay

We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.     

Computer algorithm for optimal control of linear systems with assigned eigenvalues

An efficient computer algorithm for designing optimal controllers of linear systems to have assigned closed-loop eigenvalues based on the eigenvector solution of the matrix Riccati equation is presented. The algorithm is illustrated with an example.     

Exact evaluation of responses of control systems with time delay

A method is formulated for the rapid evaluation of the response of a feedback control system with time delay to a deterministic input. The solution is obtained analytically from that of an auxiliary system without time delay. The method is exact and is generally applicable to all linear systems with constant coefficients.