Constant feedback stabilization of discrete-time systems with random-coefficients†

A method is proposed to effectively stabilize discrete-time systems involving random coefficients. The stability results are both of sample solutions and second moments of system states. The method is handy in that any finite number of steps of a Riccati-like difference equation is sufficient to guarantee the construction of a stabilizing feedback gain. The results are given for cases both with and without the presence of an additive noise term. An easy-to-test stabilizability condition accompanies the method, enhancing its utility.     

Implications of a result on observer design for stochastic parameter systems

An earlier result on observer design for stochastic parameter systems is utilized to show that optimal one-step predictors for such systems are mean square stable and to propose a new class of stable estimation schemes.     

FATE OF AFLATOXIN M1 IN KASHAR CHEESE

The distribution and stability of aflatoxin M₁ (AFM₁) in Kashar cheese were investigated. Raw milk samples were spiked with AFM₁ at the levels of 50, 250 and 750 ng/L. Distribution of toxin in milk, cheese curd, whey, kneading brine and cheese, and its stability during ripening were determined by high‐performance liquid chromatography. Concentrations of AFM₁ in curds for each contamination level were 2.93, 3.19 and 3.37 times higher than those in milk. After syneresis, the percentage distribution of AFM₁ was 40–46% in curds and 53–58% in whey indicating that relatively higher concentration of toxin passed to whey. Moreover, by the kneading process approximately 2–5% of AFM₁ passed to kneading brine. Compared to the initial spiking level, the percentage of toxin in cheeses varied between 35–42%. Over a 60‐day storage period, there was no decrease in the concentration of AFM₁, suggesting that the toxin was stable during ripening.     

Dynamic feedback control of stochastic-parameter systems

In this work, the problem of stabilizing a discrete stochastic-parameter system with incomplete state information is addressed. In order to solve this problem, a time-invariant compensator system composed of a constant gain observer and a constant feedback gain, is proposed. The stabilizability conditions depend both on the first and second moments of the stochastic parameters.     

Observer design for discrete and continuous non-linear stochastic systems

An observer design methodology that is applicable to a general class of non-linear stochastic system and measurement models is given. It is proved that, under the conditions given, discrete- and continuous-time state estimation is possible with guaranteed exponential rate of convergence. The superior performance of the observer is illustrated with two examples.     

Observer design for stochastic-parameter systems

Constant-gain linear observer design is utilized to reconstruct the state vector of stochastic systems with both multiplicative and additive noises. It is shown that if the system model is mean square stable, then it is very easy to design an effective estimation scheme     

Reduced-order control of systems disturbed by randomly correlated noise sequences

In this work, linear time-invariant discrete-time systems acted on by correlated-noise disturbances with uncertain models are mean-square stabilized by reduced-order controllers.     

Design of observers for non-linear time-varying systems

Novel stable observers are proposed for discrete, time-varying systems having time-varying, sector-bounded non-linearities. First, the form of the non-linearity is assumed to be known for all time and a stable non-linear filter is presented. Then assuming that the form of the non-linearity is not known but only a sector bound is given, we propose a linear filter and an upper bound on the sector constant to obtain a stable observer. The convergence conditions for the proposed observers are given directly in terms of the design parameters and are, therefore, very easy to check.     

New approach to observer design for two-dimensional systems

A new method of observer design for shift-invariant two-dimensional digital systems is presented. The method is applicable to a large class of two-dimensional systems and the condition of applicability is very simple to test.     

Linear state estimators for non-linear stochastic systems with noisy non-linear observations

The design of linear filters is considered for reconstructing the state of a class of discrete-time non-linear stochastic systems using noise-corrupted measurements. It is shown that for systems with mean-square stable dynamics, it is always possible to guarantee stable estimation schemes. This result is used to prove that a mean–square optimal one-step predictor has stable error dynamics and also to generate other stable predictors.