It was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable Lie algebra possesses a quadratic common Lyapunov function, which implies that the corresponding switched linear system is exponentially stable for arbitrary switching. In this paper we prove that the same properties hold under the weaker condition that the Lie algebra generated by give...

In this paper we provide conditions for the stability of discrete time switched linear systems. We accomplish this by calculating the mean and covariance of the set of matrices obtained by using all possible switching sequences. The theory of switched linear systems has received considerable attention in the systems theory literature in the last two decades. However, for discrete time switched ...

It was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable Lie algebra possesses a quadratic common Lyapunov function, which implies that the corresponding switched linear system is exponentially stable for arbitrary switching. In this paper we prove that the same properties hold under the weaker condition that the Lie algebra generated by give...

A passive system with positive definite storage function is not only stable but is intrinsically robustly stable with respect to a wide class of feedback disturbances. For linear time invariant systems, passivity can be characterized either in time domain or in frequency domain frompositive realness. This paper aims to generalize this concept to continuous-time switched linear systems. Analysis...

Pulse is often used to excite biological systems. The inputs such as irrigation, therapy, and treatments to biological systems are also equivalent to pulses. This makes the biological system behave as switched models under the function of the input. To reduce difficulty in model parameter estimation, the system could be represented as a switched linear model under the pulse excitation. In this ...

Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are neede...

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. Positive linear systems are defined on cones and not on linear spaces. Therefore, the theory of positive ...

This paper develops a new method of integral sliding mode control redesign for a class of perturbed nonlinear dissipative switched systems by modifying the dissipativity-based control law that was designed for the unperturbed systems. The nominal model is considered affine with matched and unmatched perturbations. The redesigned control law includes an integral sliding-based control signal such...

In this monograph we consider the class of continuous-time positive switched systems. We discuss several problems, including stability, performance analysis, stabilization via switching control, and optimization. The monograph starts with a chapter where several application examples are provided, to motivate the interest in this class of systems. The rest of the monograph is dedicated to the th...