Stabilization Based Networked Predictive Controller Design for Switched Plants

Stabilizing state feedback controller has been designed in this paper for a switched DC motor plant, controlled over communication network. The switched system formulation for the networked control system (NCS) with additional switching in a plant parameter along with the switching due to random packet losses, have been formulated as few set of non-strict Linear Matrix Inequalities (LMIs). In order to solve non-strict LMIs using standard LMI solver and to design the stabilizing state feedback controller, the Cone Complementary Linearization (CCL) technique has been adopted. Simulation studies have been carried out for a DC motor plant, operating at two different sampling times with random switching in the moment of inertia, representing sudden jerks.

💡 Research Summary

The paper addresses the problem of stabilizing a switched DC‑motor plant that is controlled over a communication network subject to random packet losses. In addition to the network‑induced switching (packet loss), the plant itself experiences abrupt changes in its moment of inertia, representing sudden load variations. The authors model the overall system as a discrete‑time switched system whose state transition matrix depends on two independent switching signals: one representing the number of consecutive dropped packets (σ) and another representing the current load configuration (indexed by l).

A predictive state‑feedback controller is proposed. At each sampling instant the controller computes the present control input and the next two future inputs (assuming a maximum of two consecutive packet drops). These control vectors are stored in a buffer and transmitted to the actuator; if a packet is lost, the actuator uses the pre‑computed future input. The control law is u(k)=K_q x(k), where K_q is selected according to the current σ value.

Stability is analyzed using a quadratic Lyapunov function V(k)=x̄(k)ᵀP x̄(k) (with an augmented state x̄ that includes the buffered future inputs). The condition V(k+1)−V(k)<0 for all admissible σ leads to the matrix inequality Φ(σ)ᵀP Φ(σ)−P<0, where Φ(σ) is the augmented system matrix. Because Φ(σ) depends linearly on the controller gain K, the inequality is bilinear in P and K and cannot be expressed directly as a strict LMI.

To overcome this, the authors employ the Cone Complementarity Linearization (CCL) technique. The bilinear inequality is transformed into a pair of LMIs together with a trace minimization objective: find symmetric positive‑definite matrices P and Q such that
0 ≤