S. Sathananthan

Robust adaptive control of nonaffine nonlinear plants with small input signal changes

Assuming small input signal magnitudes, ARMA models can approximate the NARMA model of nonaffine plants. Recently, NARMA-L1 and NARMA-L2 approximate models were introduced to relax such input magnitude restrictions. However, some applications require larger input signals than allowed by ARMA, NARMA-L1 and NARMA-L2 models. Under certain assumptions, we recently developed an affine approximate model that eliminates the small input magnitude restriction and replaces it with a requirement of small input changes. Such a model complements existing models. Using this model, we present an adaptive controller for discrete nonaffine plants with unknown system equations, accessible input-output signals, but inaccessible states. Our approximate model is realized by a neural network that learns the unknown input-output map online. A deadzone is used to make the weight update algorithm robust against modeling errors. A control law is developed for asymptotic tracking of slowly varying reference trajectories.

Feedback Stabilization of Markov Jump Linear Systems with Time-Varying Delay

Abstract A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Sufficient conditions for stability based on linear matrix inequalities (LMIs) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-independent. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.

Perceptually tuned robust watermarking scheme for digital images

In this paper, we present a digital image watermarking scheme that uses both human visual system and statistical properties. The scheme places watermark in discrete cosine transform (DCT) domain and spreads the watermark effect on the entire image. We have compared our proposed scheme with two other popular schemes and shown that our proposed scheme yields better results in terms of transparency, robustness and maximal capacity requirements.

Delay-dependent Stability Criteria for Markovian Switching Networks with Time-varying Delay

Abstract A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Delay-dependent sufficient conditions for stability based on linear matrix inequalities (LMIs) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-dependent. The robustness results of such stability concept against all admissible uncertainties are also investigated. This new delay-dependent stability criteria is less conservative than the existing delay-independent stability conditions. An example is given to demonstrate the obtained results.

Robust stability and stabilization of a class of nonlinear discrete time stochastic systems: An LMI approach

Abstract A problem of robust state feedback stability and stabilization of nonlinear discrete-time stochastic processes is considered. The linear rate vector of a discrete-time system is perturbed by a nonlinear function that satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of nonlinear discrete-time systems and, at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable. The state dependent diffusion is modeled by a normal sequence of identically independently distributed random variables. The new formulation provides a suitable setting for robust stabilization of nonlinear discrete-time systems where the underlying deterministic systems satisfy the generalized matching conditions. Our method which is based on linear matrix inequalities (LMIs) is distinctive from the existing robust control and absolute stability techniques. Examples are given to demonstrate the obtained results.

Perceptually tuned video watermarking scheme using motion entropy masking

We present a watermarking scheme for digital videos that are based on the human visual system characteristics. Our watermarking scheme inserts a perceptually invisible watermark in the discrete cosine transform (DCT) domain. We have shown that the proposed scheme provides better results than two other popular schemes both in transparency and robustness.

Stability and convergence via Lyapunov-like functionals of stochastic parabolic partial differential equations

In this paper, we employ comparison principle and Lyapunov-like functional techniques to study the convergence and stability behavior of diffusion systems in a random environment. The system is modelled using the Ito-type stochastic parabolic partial differential equations. Sufficient conditions for various concepts of stability and convergence such as the pth moment, in probability, and asymptotic stability of the solution process of the system are obtained. These sufficient conditions are based on the M-matrix tests including the diagonal dominance which are well known for its robustness implications. Moreover, an example is provided to illustrate the significance of the presented results.

Optimal Guaranteed Cost Control of Stochastic Discrete-Time Systems with States and Input Dependent Noise Under Markovian Switching

A problem of robust guaranteed cost control of stochastic discrete-time systems with parametric uncertainties under Markovian switching is considered. The control is simultaneously applied to both the random and the deterministic components of the system. The noise (the random) term depends on both the states and the control input. The jump Markovian switching is modeled by a discrete-time Markov chain and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Using linear matrix inequalities (LMIs) approach, the robust quadratic stochastic stability is obtained. The proposed control law for this quadratic stochastic stabilization result depended on the mode of the system. This control law is developed such that the closed-loop system with a cost function has an upper bound under all admissible parameter uncertainties. The upper bound for the cost function is obtained as a minimization problem. Two numerical examples are given to demonstrate the potential of the proposed techniques and obtained results.

Robust control of stochastic systems with noise dependent states and inputs under Markovian switching

A problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching and random diffusion (noise) is considered. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. Sufficient conditions based on linear matrix inequalities (LMIs) for stochastic stability is obtained. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.

Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

Abstract A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Delay-dependent sufficient conditions for stability based on linear matrix inequalities (LMIs) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-dependent. The robustness results of such stability concept against all admissible uncertainties are also investigated. This new delay-dependent stability criteria is less conservative than the existing delay-independent stability conditions. An example is given to demonstrate the obtained results.