Abraham H. Haddad

Controllability and observability of hybrid systems

Abstract A special class of hybrid systems is considered, whose state space is a cross-product space of a euclidean space and a finite-state space. Such models may be used to represent systems subject to known abrupt parameter variations, such as commu- tated networks. They may also be used to approximate some types of time-varying systems. Controllability, observability and stability of hybrid systems are inves- tigated. In particular, a necessary and sufficient algebraic condition, a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived. Moreover, a simple sufficient stability condition is provided.

Control of jump linear systems having semi-Markov sojourn times

A jump linear system (JLS) is a linear differential equation with N possible sets of randomly jumping (switching) coefficients. The JLS model has many real-world physical and conceptual (e.g. economic) systems. The bulk of the JLS-research effort concerns pure-Markov JLS (MJLS). In this paper we consider the more general semi-Markov JLS (SMJLS). This paper also shows a new sub-optimal but tractable and parsimonious control design method for SMJLS, and a closed-loop stability test.

Averaging, aggregation and optimal control of singularly perturbed stochastic hybrid systems

This paper develops methodologies for the averaging, aggregation and optimal control of stochastic hybrid systems whose state equations depend on continuoustime, nearly completely decomposable finite state Markov chains. Such Markovian switching models are assumed to have several identified groups of strongly interacting states. The random sample solution process of the system state can be well approximated by a deterministic trajectory, for the duration of an interval of which the switching process sojourns in a group. Aggregated models are obtained by utilizing the aggregation method over the infinite time interval. By using the perturbation approach, necessary and sufficient conditions of stochastic stabilizability and controllability proposed by Ji and Chizeck (1990) are presented for the systems. With the aggregation models and the known results of stochastic stabilizability, near-optimum finite time and infinite time Markovian jump linear quadratic control laws are also investigated. The limiting be...

Stability criteria for linear periodic switched systems

A fundamental matrix inequality is used to improve upon existing stability bounds for linear periodic switched systems. The inequality is further used to derive an upper stability bound for the singular perturbation parameter in the case of linear periodic singularly perturbed switched systems.

An adaptive direct-sequence spread-spectrum receiver for burst type interference

The hybrid system is an extension of the state-space system model which allows for random and abrupt changes in the model parameters. In this paper we use the hybrid system to model burst type interference in a direct-sequence spread-spectrum (DS/SS) communication system. The resulting optimum receiver is easily derived but too computationally complex to be practical. Two suboptimal but more practical receivers are presented. In an example, the hybrid system is used to model pulsed narrowband interference. The performance of each suboptimal receiver is evaluated using computer simulations. >

On Largest Lyapunov Exponent Assignment and Almost Sure Stabilization of Hybrid Systems

This paper develops techniques for the analysis, control and stabilization of hybrid systems. These systems switch among a finite set of linear time-invariant models with switching behavior governed by a Finite State Markov Chain. The relationship of these techniques to standard methodologies for linear time-invariant systems is also considered.

Stabilization of stochastic quantized control systems

This paper considers a feedback control system where a plant is actuated by a quantized control. The measurements are assumed to be disturbed by an additive wideband Gaussian noise. The nonlinear control is obtained by the quantization of the measurements and it may cause the system to be variable structure in the presence of the noise. Variable structure systems disturbed by the noise exhibit sliding modes on the switching manifold. When the system is unstable, linear optimal controls using linear-quadratic-Gaussian (LQG) formulation are investigated to stabilize the system in a region around the origin while the quantized control guides the system to the region. The performance and behavior of the stabilized systems are examined via a quadratic performance index in the steady state.

Optimal constant gain control of jump-linear systems with discrete state uncertainty

Jump-linear systems are dynamic systems with abrupt switches among several linear models, conditioned on an underlying finite state Markov process. This paper is concerned with optimal control of jump-linear systems when the discrete Markov process is not directly observable. Necessary conditions for optimality are found and a local algorithm to obtain such solutions is derived.<<ETX>>

Approximation and decomposition of singularly perturbed stochastic hybrid systems

This paper considers a singularly perturbed stochastic hybrid system whose state equations are governed by a stochastic switching process, which is modelled as a nearly completely decomposable continuous time finite state Markov chain. Approximate models for the slow mode subsystem are derived over the intervals of rapid switching and their accuracy (the mean-squared errors between the approximate models and the original systems) is quantified. Aggregate models for the subsystem are obtained over a longer period. The almost surely exponential stability of the subsystem is studied. The behaviour of the fast subsystem which depends on the relative size of the perturbation parameters is analysed. The decomposition of the overall system and the switching process together into slow and fast subsystems is investigated. The results derived in the paper are shown to hold when the switching process is stationary and irreducible, and each group of strongly interacting states is irreducible and time reversible. Fina...

Dynamic bandwidth allocation algorithm for a mixed traffic network

Considers a TDMA system designed for voice traffic, and analyzes the effects of adding data services with a specific bandwidth allocation protocol. This protocol stipulates priority for voice and movable traffic boundaries, and allocates slots at designated update interval times. A controlled Markovian analytical model is developed and used to derive relevant system performance characteristics for voice and data traffic. Additionally, the model is used to explore the optimization of system parameters to maximize data capacity subject to specified voice traffic characteristics.